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Use the Polygon Angle-Sum Theorem. How many sides does the polygon have?
79^(∘)
We have been given the following figure.
We want to find the missing angle measure z. Recall the Polygon Angle-Sum Theorem.
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Polygon Angle-Sum Theorem |
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The sum of the measures of the interior angles of a convex n-gon is (n-2)*180^(∘). |
We can tell that one of the angles is a right angle. Therefore, its measure is 90. We are given the measures of the other interior angles of the polygon, so we can write an equation where the sum of the interior angles is equal to (n-2)180. 90+112+z+79= (n-2)180 Our polygon has 4 sides, so we can substitute 4 for n and solve our equation to find z. Let's solve it to find x.