Question

Three of the interior angle measures of a pentagon are 110°, 115°, and 145°. The remaining angles are congruent. Find the measure of one of the remaining angles.

Answer 1

265°

Explanation:

First of congruent shapes are the same, meaning they angles are also the same.

⁘ 110° + 115° + 145° + 2x° = (5 x 180)°

Reason - Sum of angles in a polygon = [n-2] x 180; where n = no. of sides

⁘ 370° + 2x° = 900°

⁘ 2x° = 900° - 370°

⁘ 2x° = 530°

⁘ x° =
`(530)/(2)`

⁘ x° = 265°