Grade 7 Geometry: Angle Relationships

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Angles A and B are complementary. Angle A measures 61°. What is the measure of angle B, in degrees?

   1. Complementary angles add up to 90°.
   2. Angle B = 90° − 61° = 29°.

   Answer: 29

2. Example 2

   Two lines intersect, forming four angles. One angle measures 103°. What is the measure of the angle vertical to it (directly across the intersection), in degrees?

   1. Vertical angles sit directly across from each other where two lines cross.
   2. Vertical angles are equal, so the angle measures 103°.

   Answer: 103

3. Example 3

   Two vertical angles measure (5x + 5)° and 70°. What is the value of x?

   1. Vertical angles are equal, so set the measures equal.
   2. 5x + 5 = 70
   3. 5x = 65
   4. x = 65 ÷ 5 = 13

   Answer: 13