7.G.B.5 7th Grade Geometry

Angle Relationships

Use facts about supplementary, complementary, vertical, and adjacent angles to write and solve simple equations for an unknown angle.

How to explain it

The anchor students hold onto: Vertical angles are EQUAL. Linear pair SUMS TO 180°. Complementary SUMS TO 90°. Identify the relationship, write the equation, solve for the unknown.

Students need this skill to work with parallel lines cut by a transversal in 8.G.A.5, where vertical and supplementary relationships generalize to corresponding and alternate angle pairs.

Worked examples

Example 1 Vertical Angles

Vertical: ∠1=30°. Find ∠3.

Step 1Vertical angles are EQUAL.

Step 2∠3 and ∠1 are vertical at O.

Step 3∠3 = ∠1 = 30°.

Answer∠3 = 30°.

Example 2 Linear Pair

Linear pair: ∠1=30°. Find ∠2.

Step 1Linear pair SUMS TO 180°.

Step 2∠1 + ∠2 = 180°.

Step 330° + ∠2 = 180°.

Step 4∠2 = 150°.

Answer∠2 = 150°.

Example 3 Complementary

OE⊥AB: ∠BOC=30°. Find ∠COE.

Step 1∠BOE = 90° (right angle).

Step 2∠BOC + x = 90°.

Step 330° + x = 90°.

Step 4x = 60°.

Answerx = 60° (∠COE).

Common mistakes

What students write Student confuses complementary (90°) and supplementary (180°) — writes the wrong sum in the equation.

The fix Complementary = 90° (right angle). Supplementary = 180° (straight line). Identify the figure first.

What students write Student writes ∠1 = ∠2 for a linear pair — treats it as vertical angles instead of a sum equation.

The fix Linear pair angles are on the same straight line — write the SUM equation: ∠1 + ∠2 = 180°.

Teacher tip

Head off the two predictable errors before they happen. First: Complementary = 90° (right angle). Supplementary = 180° (straight line). Identify the figure first. Second: Linear pair angles are on the same straight line — write the SUM equation: ∠1 + ∠2 = 180°.