{"id":94,"date":"2022-04-13T08:19:27","date_gmt":"2022-04-13T08:19:27","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=94"},"modified":"2025-09-02T02:51:23","modified_gmt":"2025-09-02T02:51:23","slug":"f-2-transversals-of-parallel-lines-find-angle-measures","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/f-2-transversals-of-parallel-lines-find-angle-measures\/","title":{"rendered":"F.2 Transversals of parallel lines: find angle measures"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Transversals of parallel lines: find angle measures<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwiXdIp2Y\/Dw95Jn3SvwyUBZU1N0nRhg\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwiXdIp2Y&#x2F;Dw95Jn3SvwyUBZU1N0nRhg&#x2F;watch?utm_content=DAGwiXdIp2Y&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">transversals of parallel lines find angle measures<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong> Key Concepts<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Parallel Lines and Transversal<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Parallel Lines:<\/strong> Two lines that never meet, no matter how far they are extended.<\/li>\n\n\n\n<li>Symbol: l\u2225m<\/li>\n\n\n\n<li><strong>Transversal:<\/strong> A line that intersects two or more lines at distinct points.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Types of Angles Formed by a Transversal<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>When a transversal cuts two parallel lines, the following types of angles are formed:<\/p>\n\n\n\n<p><strong>Corresponding Angles (\u2220)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angles in the same relative position at each intersection.<\/li>\n\n\n\n<li><strong>Property:<\/strong> Corresponding angles are <strong>equal<\/strong>.<\/li>\n\n\n\n<li>Example: \u22201=\u22205<\/li>\n<\/ul>\n\n\n\n<p><strong>Alternate Interior Angles<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angles on opposite sides of the transversal, <strong>inside<\/strong> the parallel lines.<\/li>\n\n\n\n<li><strong>Property:<\/strong> Alternate interior angles are <strong>equal<\/strong>.<\/li>\n\n\n\n<li>Example: \u22203=\u22206<\/li>\n<\/ul>\n\n\n\n<p><strong>Alternate Exterior Angles<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angles on opposite sides of the transversal, <strong>outside<\/strong> the parallel lines.<\/li>\n\n\n\n<li><strong>Property:<\/strong> Alternate exterior angles are <strong>equal<\/strong>.<\/li>\n\n\n\n<li>Example: \u22201=\u22208<\/li>\n<\/ul>\n\n\n\n<p><strong>Interior Angles on the Same Side (Consecutive Interior Angles \/ Co-Interior Angles)<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angles on the same side of the transversal, <strong>inside<\/strong> the parallel lines.<\/li>\n\n\n\n<li><strong>Property:<\/strong> Sum = 180<sup>\u2218<\/sup> (Supplementary)<\/li>\n\n\n\n<li>Example: \u22203+\u22205=180<sup>\u2218<\/sup><\/li>\n<\/ul>\n\n\n\n<p><strong>Exterior Angles on the Same Side<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Angles on the same side of the transversal, <strong>outside<\/strong> the parallel lines.<\/li>\n\n\n\n<li><strong>Property:<\/strong> Sum = 180<sup>\u2218<\/sup><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong> Steps to Find Angle Measures<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>1.<\/strong> <strong>Identify the Parallel Lines and Transversal.<\/strong><\/p>\n\n\n\n<p><strong>2.<\/strong> <strong>Label the angles<\/strong> formed at intersections.<\/p>\n\n\n\n<p><strong>3.<\/strong> <strong>Use angle relationships<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Corresponding angles \u2192 equal<\/li>\n\n\n\n<li>Alternate interior angles \u2192 equal<\/li>\n\n\n\n<li>Alternate exterior angles \u2192 equal<\/li>\n\n\n\n<li>Co-interior angles \u2192 sum = 180\u00b0<\/li>\n<\/ul>\n\n\n\n<p><strong>4 .Write equations<\/strong> if needed.<\/p>\n\n\n\n<p><strong>5. Solve for unknown angles<\/strong> using algebra.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong> Examples<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Example 1:<\/strong><br>Two parallel lines l\u2225m are cut by a transversal. One angle is 70<sup>\u2218<\/sup> Find all other angles.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Corresponding angle =70<sup>\u2218<\/sup><\/li>\n\n\n\n<li>Alternate interior angle = 70<sup>\u2218<\/sup><\/li>\n\n\n\n<li>Co-interior angle = 180\u221270=110<sup>\u2218<\/sup><\/li>\n\n\n\n<li>Alternate exterior angle = 70<sup>\u2218<\/sup><\/li>\n\n\n\n<li>Exterior angle on same side = 110<sup>\u2218<\/sup><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Example 2:<\/strong><\/p>\n\n\n\n<p><br>Two parallel lines are cut by a transversal. One angle is 2x+10<sup>\u2218<\/sup> and its corresponding angle is 70<sup>\u2218<\/sup> Find x.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Corresponding angles are equal:<\/p>\n\n\n\n<p class=\"has-text-align-center\"> 2x+10=70<\/p>\n\n\n\n<p class=\"has-text-align-center\"> 2x=60<\/p>\n\n\n\n<p class=\"has-text-align-center\">x=30<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong> Tips and Tricks<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always check if lines are parallel; the angle relationships <strong>only apply for parallel lines<\/strong>.<\/li>\n\n\n\n<li>Start by identifying known angles and using equality or supplementary relationships.<\/li>\n\n\n\n<li>Use algebra carefully for unknown angles.<\/li>\n\n\n\n<li>Draw a clear diagram; labeling makes calculations easier.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong> Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Two parallel lines are cut by a transversal. One angle measures 55<sup>\u2218<\/sup> Find all other angles.<\/li>\n\n\n\n<li>One angle formed by a transversal is 3x\u221210<sup>\u2218<\/sup>, its alternate interior angle is 50<sup>\u2218<\/sup> Find x.<\/li>\n\n\n\n<li>Find the unknown angles if two parallel lines are intersected by a transversal and one angle is 120<sup>\u2218<\/sup><\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#fccdcd\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Look at this diagram:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"502\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-7.png\" alt=\"\" class=\"wp-image-7399\" style=\"aspect-ratio:0.9957805907172996;width:342px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-7.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-7-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-7-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>if SU and VX are parallel lines and \u2220XWT = 49\u00b0 , what is \u2220VWY ?<\/strong><\/p>\n\n\n\n<p>_____ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;\u2220<strong><em>XWT<\/em><\/strong>&nbsp;and&nbsp;\u2220<strong><em>VWY<\/em><\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"499\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__9_-removebg-preview.png\" alt=\"\" class=\"wp-image-7401\" style=\"aspect-ratio:1;width:318px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__9_-removebg-preview.png 499w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__9_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__9_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 499px) 100vw, 499px\" \/><\/figure><\/div>\n\n\n<p>\u2220<em>XWT<\/em>&nbsp;and&nbsp;\u2220<em>VWY<\/em>&nbsp;are vertical angles, so they have the same measure.<\/p>\n\n\n\n<p>\u2220VWY = \u2220XWT<\/p>\n\n\n\n<p>\u2220VWY = 49\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f0d4fc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Look at this diagram:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"502\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-9.png\" alt=\"\" class=\"wp-image-7404\" style=\"width:232px;height:233px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-9.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-9-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled-design-9-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>if EG and HJ are parallel lines and \u2220HIK = 48\u00b0 , what is \u2220JIF ?<\/strong><\/p>\n\n\n\n<p>_____ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;\u2220<strong><em>HIK<\/em><\/strong>&nbsp;and&nbsp;\u2220<strong><em>JIF<\/em><\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"499\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__2_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-7406\" style=\"width:228px;height:228px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__2_-removebg-preview-1.png 499w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__2_-removebg-preview-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Untitled_design__2_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 499px) 100vw, 499px\" \/><\/figure><\/div>\n\n\n<p>\u2220<em>HIK<\/em>&nbsp;and&nbsp;\u2220<em>JIF<\/em>&nbsp;are vertical angles, so they have the same measure.<\/p>\n\n\n\n<p>\u2220JIF = \u2220HIK<\/p>\n\n\n\n<p>\u2220JIF = 48\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#d0f7e1\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Look at this diagram:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3.png\" alt=\"\" class=\"wp-image-8431\" style=\"width:233px;height:233px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled-design-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>If JL and MO are parallel lines and \u2220JKI = 137\u00b0, what is \u2220LKI?<\/strong><\/p>\n\n\n\n<p>_____\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;\u2220<strong><em>JKI<\/em><\/strong>&nbsp;and&nbsp;\u2220<strong><em>LKI<\/em><\/strong>.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview.png\" alt=\"\" class=\"wp-image-8432\" style=\"width:236px;height:236px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/06\/Untitled_design__4_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2220<em>KI<\/em>&nbsp;and&nbsp;\u2220<em>LKI<\/em>&nbsp;are supplementary angles, so their measures add up to 180\u00b0.<\/p>\n\n\n\n<p><img decoding=\"async\" src=\"https:\/\/in.ixl.com\/qgen_res\/math\/math_symbols\/angle.png\"><em>JKI<\/em>&nbsp;+&nbsp;<img decoding=\"async\" src=\"https:\/\/in.ixl.com\/qgen_res\/math\/math_symbols\/angle.png\"><em>LKI<\/em>&nbsp;= 180\u00b0<\/p>\n\n\n\n<p>Substitute \u2220JKI = 137\u00b0 and solve.<\/p>\n\n\n\n<p>137\u00b0 + \u2220LKI = 180\u00b0<\/p>\n\n\n\n<p>\u2220LKI = 180\u00b0 &#8211; 137\u00b0<\/p>\n\n\n\n<p>\u2220LKI = 43\u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/96174\/657\/774\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-32.png\" alt=\"\" class=\"wp-image-7407\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-32.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-32-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-32-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/35813\/917\/147\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-35.png\" alt=\"\" class=\"wp-image-7408\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-35.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-35-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-35-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Transversals of parallel lines: find angle measures transversals of parallel lines find angle measures by Delta publications key notes : Key Concepts Parallel Lines and Transversal Types of Angles Formed by a Transversal When a transversal cuts two parallel lines, the following types of angles are formed: Corresponding Angles (\u2220) Alternate Interior Angles Alternate Exterior<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/f-2-transversals-of-parallel-lines-find-angle-measures\/\">Continue reading <span class=\"screen-reader-text\">&#8220;F.2 Transversals of parallel lines: find angle 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