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vlada-n [284]
3 years ago
6

The measure of an exterior angle of a regular polygon is 45. What is the interior angle and how many sides?

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
3 0

Check the picture below.

\bf \textit{sum of all exterior angles in a polygon}\\\\ n\theta = 360~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ 0=45 \end{cases}\implies n(45)=360\implies n=\cfrac{360}{45}\implies \stackrel{\textit{an octagon}}{n=8}

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