Is it possibale for the interior angles of a regualr polygon to each measure 170 a.true b.false

Question

asked Mar 22, 2024 94.6k views

1 Answer

Egor Nepomnyaschih · Answer 1 · 2024-03-29T08:57:00+0000

Step-by-step explanation

For regular polygons, the interior angle formula is

i = 180(n-2)/n

where n is the number of sides. Let's replace the 'i' with 170 and solve for n.

i = 180(n-2)/n

170 = 180(n-2)/n

170n = 180(n-2)

170n = 180n-360

170n-180n = -360

-10n = -360

n = -360/(-10)

n = 36

We see that an interior angle of 170 degrees is possible. It happens when the regular polygon has 36 sides.

Check:

i = 180(n-2)/n

i = 180(36-2)/36

i = 170

The answer is confirmed.