Question

A wooden plate is shaped as a pentagon. The measure of one angle is 60°. The remaining interior angles are obtuse and of equal measure.

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

105°

120°

96°

135°

Answer 1

From http://www.mathsisfun.com/geometry/interior-angles-polygons.html

The sum of the interior angles of a polygon:
\[(n-2) *180°\]
since you have a pentegon you would substitute 5 into n and obtain:
\[SumOfAngle = 540^o\]
remove the 60 degrees for the given angle and share the remaining degrees evenly across the four other angles.