Question

The measure of each interior angle of a regular polygon is 140 then the number of sides the regular polygon has

Answer 1

Answer:

Measure of interior angle = 140°

180 - 140 = 40°

= $\frac{360}{40}$

= 9

∴ The number of sides the polygon has = 9

Answer 2

Answer:

9 sides

Step-by-step explanation:

Size of each interior angle = 180° * (n – 2)/n

Therefore, 140° = 180° * (n – 2)/n

Multiply both sides by n

140°n =180° (n – 2)

140°n = 180°n – 360°

Subtract both sides by 180°n.

140°n – 180°n = 180°n – 180°n – 360°

-40°n = -360°

Divide both sides by -40°

n = -360°/-40°

= 9.

Therefore, the number of sides is 9 (nonagon)