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°

120 degrees

Step-by-step explanation:

The angles in a pentagon add up to 540 degrees. This means that we can set up an equation to find this. We'll call the measure of the angle that we want to find x.

112+68+3x=540

Solving this, we get 180+3x=540, and 3x=360. That means that x is 120 degrees.