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Polygon Interior Angles
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Polygon Interior Angles
Show your working for calculation questions. Give angle answers in degrees.
Using the interior-angle sum
1.Find the sum of the interior angles of a triangle.
2.Find the sum of the interior angles of a quadrilateral.
3.Find the sum of the interior angles of a pentagon.
4.Find the sum of the interior angles of a hexagon.
5.Which polygon has an interior-angle sum of 1,260°?
- Heptagon
- Octagon
- Nonagon
- Decagon
6.Calculate the sum of the interior angles of a 14-sided polygon. Show your working.
Finding unknown angles
7.Three interior angles of a quadrilateral are 78°, 104° and 91°. Find its fourth interior angle.
8.Four interior angles of a pentagon measure 101°, 116°, 94° and 128°. Calculate the fifth angle.
9.A hexagon has five interior angles of 117°, 124°, 109°, 132° and 121°. What is the sixth angle?
- 117°
- 127°
- 137°
- 147°
10.A heptagon has six interior angles of 130°, 140°, 125°, 138°, 132° and 135°. Find the seventh angle.
Reasoning and regular polygons
11.A regular polygon has interior angles of 150° each. How many sides does it have?
12.A regular polygon has an interior-angle sum of 1,440°. Find its number of sides and the size of each interior angle.
13.True or false: increasing a polygon's number of sides by one increases its interior-angle sum by 180°.
TrueFalse
14.A student says a regular polygon with an interior angle of 160° must have 18 sides. Check the claim and give the correct number of sides, showing why.
15.Match each polygon to its interior-angle sum.
- Octagon (8 sides)
- Decagon (10 sides)
- Dodecagon (12 sides)
- Nonagon (9 sides)
- 1,260°
- 1,080°
- 1,440°
- 1,800°
3 printable pages
Page 1
Page 2
Page 3
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