Grade 7 Geometry: Unit Review

Worked examples

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

1. Example 1

   A circle has a circumference of 18.84 meters. What is its diameter, in meters? Use 3.14 for π.

   1. Start from C = πd, so d = C ÷ π.
   2. d = 18.84 ÷ 3.14 = 6.

   Answer: 6

2. Example 2

   Two vertical angles measure (2x + 15)° and 133°. What is the value of x?

   1. Vertical angles are equal, so set the measures equal.
   2. 2x + 15 = 133
   3. 2x = 118
   4. x = 118 ÷ 2 = 59

   Answer: 59

3. Example 3

   A right triangle has one acute angle that measures 24°. What is the measure of the other acute angle, in degrees?

   1. The angles of a triangle add up to 180°, and the right angle is 90°.
   2. 180° − 90° − 24° = 66°.

   Answer: 66