A road sign is in the shape of a regular decagon. What is the measure of each angle on the sign?

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Answer 1 · 2017-08-04T21:15:00

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$m ∠ = 144^{o}$ $m/_=144^o$

the formula to find the measure of the interior angles of a regular polygon is

$m ∠ = \frac{(n - 2) \cdot 180}{n}$ $m/_=[(n-2)*180]/n" "$ where $n =$ $n=$ the number of sides

A decagon has $10$ $10$ sides so $n = 10$ $n=10$

$m ∠ = \frac{(10 - 2) \cdot 180}{10}$ $m/_=[(10-2)*180]/10$

$m ∠ = \frac{(8) \cdot 180}{10}$ $m/_=[(8)*180]/10$

$m ∠ = \frac{1440}{10}$ $m/_=1440/10$

$m ∠ = 144^{o}$ $m/_=144^o$