Question
The adjacent interior and exterior angles of a polygon are supplementary, as indicated in the drawing. Assume that you know that the measure of each interior angle of a regular polygon is $\frac{(n-2) 180}{n}$. a) Express the measure of each exterior angle as the supplement of the interior angle.b) Simplify the expression in part(a) to show that each exterior angle has a measure of $\frac{360}{n}$. (FIGURE CAN'T COPY)
Step 1
Since the interior and exterior angles are supplementary, the measure of each exterior angle is the supplement of the interior angle. Therefore, the measure of each exterior angle is $180 - \frac{(n-2) 180}{n}$. Show more…
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The exterior angle of a triangle is the supplement of an interior angle. Show that the sum of the exterior angles of a triangle always adds up to 360. The diagram shows a triangle with its interior angles and their supplements (which are the exterior angles). In general, find the sum of the exterior angles of a polygon with sides. This is a pretty cool result!
CHALLENGE Two formulas can be used to find the measure of an interior angle of a regular polygon: $$s=\frac{180(n-2)}{n}$ and $s=180-\frac{360}{n} $$. Show that these are equivalent.
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