Worked example
What is the sum in degrees of the interior angles of a 5-sided simple convex polygon?
Answer & why
Answer: 540
Draw diagonals from one vertex to form 3 triangles. Their angles total 3 × 180 = 540°.
Grade 8 · Math
Find a polygon’s interior-angle sum
Use a triangle decomposition to find an angle sum.
8 authored questions + worked example
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All questions
All 8 authored questions for this skill.
Question 1
What is the sum in degrees of the interior angles of a 11-sided simple convex polygon?
- 1620
- 1619
- 1621
- 1622
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 1620
Draw diagonals from one vertex to form 9 triangles. Their angles total 9 × 180 = 1620°.
Question 2
What is the sum in degrees of the interior angles of a 12-sided simple convex polygon?
- 1799
- 1801
- 1802
- 1800
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 1800
Draw diagonals from one vertex to form 10 triangles. Their angles total 10 × 180 = 1800°.
Question 3
What is the sum in degrees of the interior angles of a 5-sided simple convex polygon?
- 539
- 540
- 541
- 542
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 540
Draw diagonals from one vertex to form 3 triangles. Their angles total 3 × 180 = 540°.
Question 4
What is the sum in degrees of the interior angles of a 6-sided simple convex polygon?
- 721
- 722
- 720
- 719
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 720
Draw diagonals from one vertex to form 4 triangles. Their angles total 4 × 180 = 720°.
Question 5
What is the sum in degrees of the interior angles of a 7-sided simple convex polygon?
- 901
- 899
- 902
- 900
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 900
Draw diagonals from one vertex to form 5 triangles. Their angles total 5 × 180 = 900°.
Question 6
What is the sum in degrees of the interior angles of a 8-sided simple convex polygon?
- 1079
- 1081
- 1080
- 1082
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 1080
Draw diagonals from one vertex to form 6 triangles. Their angles total 6 × 180 = 1080°.
Question 7
What is the sum in degrees of the interior angles of a 9-sided simple convex polygon?
- 1260
- 1259
- 1261
- 1262
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 1260
Draw diagonals from one vertex to form 7 triangles. Their angles total 7 × 180 = 1260°.
Question 8
What is the sum in degrees of the interior angles of a 10-sided simple convex polygon?
- 1441
- 1439
- 1442
- 1440
A hint
Divide the polygon into triangles from one vertex.
Answer & why
Answer: 1440
Draw diagonals from one vertex to form 8 triangles. Their angles total 8 × 180 = 1440°.