Two interior angles of a pentagon measures 112 degrees and 68 degrees and the remaining angles are of the same measures. find the measures of this angle

120°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 5 since a pentagon has 5 sides, thus

sum = 180° × 3 = 540°

let x be the measure of the 3 equal angles

Sum the interior angles and equate to 540

112 + 68 + 3x = 540, that is

180 + 3x = 540 ( subtract 180 from both sides )

3x = 360 ( divide both sides by 3 )

x = 120

Hence the measure of each equal interior angle is 120°

both equations and proportions are better.

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