In a hexagon, three angles have the same measure. The measure of each of the congruent angles is twice the measure of the fourth angle and is half the measure of the fifth angle. The sixth angle measure 115°. What is the measure of the smallest angle?

Guest May 2, 2017

#1**+2 **

The interior angles sum to 720°

So..let x be the measure of one of the congruent angles......and we have

3x + (1/2)x + 2x + 115 = 720 simplify

5.5x + 115 = 720 subtract 115 from each side

5.5x = 605 divide both sides by 5.5

x = 110

The smallest angle = (1/2)x = (1/2) * 110 = 55°

CPhill
May 3, 2017