Question

A particular convex pentagon has two congruent, acute angles. The measure of each of the other interior angles is equal to the sum of the measures of the two acute angles. What is the common measure of the large angles, in degrees?

Answer 1

1. First, you must apply the formula for calculate the sum of the interior angles of a regular polygon, which is shown below:

 (n-2) × 180°

 "n" is the number of sides of the polygon (n=5).

 2. Then, the sum of the interior angles of the pentagon, is:

 (5-2)x180°=540°

 3. The problem says that the measure of each of the other interior angles is equal to the sum of the measures of the two acute angles and now you know that the sum of all the angles is 540°, then, you have:

 α+α+2α+2α+2α=540°

 8α=540°

 α=540°/8

 α=67.5°

 4. Finally, the larger angle is:

 2α=2(67.5°)=135°

 5. Therefore, the answer is: 135°