A wooden plate is shaped as a pentagon. The measure of one angle is 80°. The remaining interior angles are obtuse and of equal measure.

What is the measure of each obtuse angle in the pentagon?

92°

160°

115°

135°

Question

A wooden plate is shaped as a pentagon. The measure of one angle is 80°. The remaining interior angles are obtuse and of equal measure.  
 
What is the measure of each obtuse angle in the pentagon?

 92°

 160°

 115°

 135°

anonymous · Answer

pentagon can be divided into 3 triangles.  Since each triangle has an angle sum of 180 that makes 540 degrees total.  We know that one angle is 80 so that leaves 540-80=460 for the remaining 4 angles.  Since 460/4=115, choose that answer.

campbell_st · Answer

the angles sum of a pentagon is 540 degrees

if 1 angle is 80 then the other 4 angles add to 

540 - 80 = 460 degrees

if they remaining angles are obtuse and equal then 

460/4 = 115 degrees