What is the sum of the degrees of the exterior angles of a convex pentagon

Mathematics

1 answer:

Fofino [41]2 years ago

5 0

Answer:

The sum of the measures of the exterior angles of a convex polygon is 360 degrees.

Step-by-step explanation:

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Find the measure of one interior angle of a regular 14-gon.

lozanna [386]

$\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n=\stackrel{polygon}{sides}\\ \theta = angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ n = 14\\ \end{cases}\implies 14\theta =180(14-2) \\\\\\ 14\theta =180(12)\implies 14\theta =2160\implies \theta =\cfrac{2160}{14}\implies \theta \approx 154.3^o$