Question

Each of the angles of a polygon is 140°. Find the number of sides the polygon has

Answer 1

Solution:

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).

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