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each interior angle of a regular polygon measures 156°. how many sides does the polygon have?
we know that each angle in a regular polygon is given by the formula angle=(180)(n-2)/n where is number of sides we actually have the angle, so we can write 156=(180)(n-2)/n 156*n=180 *(n-2) furthermore 156n=180n-360 360=180n-156n 360=24n n=360/24 n=15 this is a polygon with 15 sides
the angle interior formula is each interior angle=[tex] \frac{(n-2)180}{n} [/tex] where n=number of sides subsitute156= [tex] \frac{(n-2)180}{n} [\tex] multiply both sides by n 156n=(n-2)180 divide both sides by 180 13/15 times n=n-2 multiply both sides by 15 to clear fraction 13n=15n-30 subtract 13n from both sides 0=2n-30 add 30 to both sides 30=2n divide 2 15=n
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