Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
4. Polygons and Angles
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Exercise 11 Page 401

In a polygon, the sum of the measures of the exterior angles — one at each vertex — is

Practice makes perfect

We are given the following diagram.

The polygon

We are asked to find the value of Notice that the angle is one of the exterior angles of the polygon in the diagram. To find the measure of the angle, we will first recall an important piece of information.

Exterior Angles of a Polygon

In a polygon, the sum of the measures of the exterior angles — one at each vertex — is

This means that the sum of the exterior angles of the given triangle is also Let's mark an exterior angle at each vertex of this triangle.

The polygon with exterior angles marked
The exterior angles of the triangle have measures of and These measures add up to
We can use this equation to find the value of but we need to find the value of first. Notice that the angle and the angle form a straight line.
The supplementary angles
Therefore, these angles are supplementary and the sum of their measures is
Now we can solve this equation for For simplicity, we will not write the degree symbol.
Finally, we will substitue for into the first equation and solve it for
Solve for
We got that