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Example 5: Find the measure of each interior angle of the following regular polygons:

(a) Regular pentagon (b) Regular heptagon (c) Regular decagon
Solution: (a) Number of sides in a regular pentagon, n = 5
\ Sum of the interior angles of a regular pentagon = (5 – 2) × 180° (n = 5)

= 3 × 180° = 540°
540°
Therefore, the measure of each interior angle in the regular pentagon = = 108°
5
(b) Number of sides in a regular heptagon, n = 7
\ Sum of the interior angles of a regular heptagon = (7 – 2) × 180° (n = 7)

= 5 × 180° = 900°
900°
.
Therefore, the measure of each interior angle in the regular heptagon = = 128 57°
7
(c) Number of sides in a regular decagon, n = 10
Sum of the interior angles of a regular decagon = (10 – 2) × 180° (n = 10)

= 8 × 180° = 1440°
1440°
Therefore, the measure of each interior angle in the regular decagon = = 144°
10

Quick Check
Complete the given table.

Polygon Number of sides Sum of interior angles
Hexagon
Nonagon

n-gon

Sum of Exterior Angles of a Polygon

Let us draw any three different polygons and mark their exterior angles in order.

A ∠1 A ∠1 F ∠6 A
∠4 E ∠5 B ∠5 ∠1
D B ∠2 E B
∠2 ∠4 D C ∠4 ∠2
∠3 ∠3 D ∠3 C
C
Cut off the exterior angles of each polygon and arrange them together at a point as shown below:

∠1 ∠5
∠4 ∠2 ∠4 ∠5 ∠1 ∠4 ∠6
∠3 ∠3 ∠2 ∠3 ∠2 ∠1

61 Quadrilaterals