Math CentralQuandaries & Queries


Question from Mary:

If four interior angles of a five-sided figure pentagon measure 100 degrees each, what will the fifth angle measure?


I know that the sum of the exterior angles pf a polygon is 360o. I remember this because of a really neat proof that Walter Whitely sent us a while ago. It just involves walking around the perimeter of the polygon and adding up the angles of each turn at the vertices.

At each vertex the external angle measures 180o minus the internal angle. Hence for a pentagon

360o = sum of (external angles)
= sum of (180o - internal angles)
= 5 × 180o - sum of (internal angles)

What is the sum of the measures of the internal angles?


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