Angles and Polygons Assessment

Name:

Date:

📐 Part 1: Triangle Angle Properties

1. Explain why the interior angles of any triangle always add up to 180°. Use a diagram and words to support your explanation.

2. Calculate the missing angle in this triangle. Show your working.

Triangle ABC has angles: ∠A = 65°, ∠B = 47°, ∠C = ____°

3. In triangle PQR, one angle is twice as large as another, and the third angle is 60°. Find all three angles.

4. Complete the table below and write a general rule for interior angle sums.

Number of sides: 3 → 180°, 4 → ____°, 5 → ____°, 6 → ____°, n → ________

General rule: Interior angle sum = ________________

5. A regular octagon has how many sides? What is each interior angle?

6. The interior angles of a pentagon are 108°, 115°, 95°, 130°, and x°. Find the value of x.

7. What do the exterior angles of any polygon always add up to? Circle the correct answer.

180°

360°

It depends on the number of sides

8. In the diagram below, find the values of angles a, b, and c. The shape is a quadrilateral with one exterior angle shown.

Given: Interior angles are 85°, 110°, 95°, and angle a. Exterior angle b is adjacent to angle a, and angle c is vertically opposite to a 45° angle.

9. Explain why the exterior angle of any polygon at one vertex plus its adjacent interior angle always equals 180°.