Question

A wooden plate is shaped as a pentagon. The measure of one angle is 20°. The remaining interior angles are obtuse and of equal measure.

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

Answer 1

You know that a pentagon has 5 sides and 5 angles. So, if you already have one angle you only have to solve for four more, which happen to be equal. So, first determine the total degrees sum of the interior angles in a pentagon by using the formula: 180(n-2) where n is the number of sides in the polygon. So, the sum of interior angles in a pentagon is 540. And now that you have one of them, you know the sum of the remaining 4 is 540-20=520 degrees. And the problem also tells you that these last four angles are equal and obtuse! You are halfway done: just divided the remaining degrees, 520/4 and you get 130 degrees. Now check, is this obtuse? Yes, it is greater than 90 degrees but less than 180! Hope this helps!

Answer 2

140