Find measures of complementary, supplementary, vertical and adjacent angles

key notes :

Complementary Angles

• Definition: Two angles are complementary if the sum of their measures is 90°.
• Example: If one angle is 40°, the other angle is 90°−40°=50°.
• Formula:

If ∠A+∠B=90°, then ∠A and ∠B are complementary.

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🔹 Supplementary Angles

• Definition: Two angles are supplementary if the sum of their measures is 180°.
• Example: If one angle is 120°, the other angle is 180°−120°=60°
• Formula:

If ∠A+∠B=180°, then ∠A and ∠B are supplementary.

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🔹 Vertical Angles

• Definition: Vertical angles are the opposite angles formed when two lines intersect.
• Property: Vertical angles are always equal.
• Example: If two lines intersect and one angle is 75°, the opposite vertical angle is also 75°.

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🔹 Adjacent Angles

• Definition: Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.
• Example: If two angles share one arm, such as ∠ABC and ∠CBD, they are adjacent.

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📐 Key Properties to Remember

1. Complementary angles → sum = 90°.
2. Supplementary angles → sum = 180°.
3. Vertical angles → equal in measure.
4. Adjacent angles → share a common side and vertex.

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📝 Example Problems

1. If one angle is 35°, find its complement.
   → Complement = 90°−35°=55
2. If one angle is 110°, find its supplement.
   → Supplement = 180°−110°=70°
3. Two intersecting lines form one angle of 65°. Find the opposite angle.
   → Vertical angle = 65°.
4. ∠PQR = 40° and ∠RQS = 50°. Are they complementary?
   → 40°+50°=90°. Yes, they are complementary.

Learn with an example

Let’s Practice!