Identify complementary, supplementary, vertical, adjacent and congruent angles

Key Notes:

Introduction to Angles

An angle is formed when two rays share a common endpoint. The rays are called sides of the angle, and the common endpoint is called the vertex. Angles are measured in degrees (°).

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Types of Angle Relationships

Complementary Angles

Definition: Two angles are complementary if the sum of their measures is 90°.

• Formula:

• Angle A+Angle B=90∘

• Example:
• ∠P = 30°, ∠Q = 60° → ∠P + ∠Q = 90° → Complementary

Key Tip: Each angle is called the complement of the other.

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Supplementary Angles

• Definition: Two angles are supplementary if the sum of their measures is 180°.
• Formula:
• Angle A+Angle B=180^∘
• Example:
  ∠X = 110°, ∠Y = 70° → ∠X + ∠Y = 180° → Supplementary
• Key Tip: Often seen in a straight line.

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Vertical Angles (Opposite Angles)

• Definition: Vertical angles are formed when two lines intersect, creating two pairs of opposite angles.
• Property: Vertical angles are always equal.
• Example:
  If ∠1 = 50°, then the angle opposite to it ∠2 = 50°
• Key Tip: Also called opposite angles.

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Adjacent Angles

• Definition: Adjacent angles share a common vertex and a common side, but do not overlap.
• Property: The sum of adjacent angles may or may not be 90° or 180° (depends on the situation).
• Example:
  ∠A and ∠B share a vertex O and a common side → Adjacent

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Congruent Angles

• Definition: Congruent angles have the same measure.
• Symbol: ∠A ≅ ∠B
• Example:
  ∠P = 40°, ∠Q = 40° → ∠P ≅ ∠Q
• Key Tip: Congruent angles can be anywhere, not necessarily adjacent.

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Quick Reference Table

Angle Type	Definition	Formula / Property	Example
Complementary	Sum = 90°	A + B = 90°	30° + 60°
Supplementary	Sum = 180°	A + B = 180°	110° + 70°
Vertical	Opposite angles when lines intersect	∠1 = ∠2	50° and opposite 50°
Adjacent	Share a vertex and a side	May vary	∠A and ∠B share vertex O
Congruent	Same measure	∠A ≅ ∠B	40° ≅ 40°

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Tips to Identify

1. Look at the sum → 90° (complementary), 180° (supplementary).
2. Look at the position → Opposite angles (vertical), side by side (adjacent).
3. Compare measures → Same measure → Congruent.

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Practice Questions

1. Find the complement of 35°.
2. Two angles are supplementary. If one angle is 120°, find the other.
3. Identify the vertical angles in an intersecting lines diagram.
4. Find which angles are adjacent in the given figure.
5. Check if two angles measuring 55° and 55° are congruent.

Learn with an example

Let’s Practice!