One angle of a six-sided polygon is 140° and the other angles are equal. Find the measure of each equal angle.

By formula,

Sum of interior angles of an 'n' sided polygon = (2n - 4) × 90°.

Sum of interior angles of a six-sided polygon = [2 × 6 - 4] × 90°

= [12 - 4] × 90°

= 8 × 90°

= 720°.

Given,

One angle of a six-sided polygon is 140° and the other angles are equal.

∴ 140° + 5x = 720°

⇒ 5x = 720° - 140°

⇒ 5x = 580°

⇒ x = $\dfrac{580°}{5}$ = 116°.

Hence, each equal angle of a six-sided polygon = 116°.