Posted by Kay on Friday, February 17, 2012 at 12:21am.
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?

Geometry  yoyoma, Friday, February 17, 2012 at 12:28am
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(n2) 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 54020=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!

Geometry  john, Sunday, February 26, 2012 at 6:50pm
140
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