Two angles of an eight sided polygon are 142° and 176°. If the remaining angles are equal to each other; find the magnitude of each of the equal angles.

By formula,

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

Sum of interior angles of 8 sided polygon = [2 × 8 - 4] × 90°

= [16 - 4] × 90°

= 12 × 90°

= 1080°.

Given,

Two angles of an eight sided polygon are 142° and 176° and remaining angles are equal. Let each equal angle be x.

⇒ 142° + 176° + 6x = 1080°

⇒ 318° + 6x = 1080°

⇒ 6x = 1080° - 318°

⇒ 6x = 762°

⇒ x = $\dfrac{762°}{6}$ = 127°.

Hence, each equal angle = 127°.