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Geometry: Polygons

Problems

Properties of Polygons

Quadrilaterals

Problem : A regular polygon has 5 diagonals. What are the measures of its exterior angles?

The polygon is a pentagon and has five exterior angles, so the measure of each is 72 degrees.

Problem : A polygon has 7 vertices. How many diagonals does it have?

14

Problem : If a polygon has n sides, how many diagonals can be drawn from a given vertex?

n-3 diagonals

Problem : In the figure below, are angles x and y complementary?

Yes, their sum is 90 degrees.

Problem : For what kind of polygon is the sum of the exterior angles equal to the sum of the interior angles?

Quadrilaterals

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