Question

65)
The measure of one angle of a regular polygon is 135 degrees. Find the nuber of sides.

a) 4
b) 6
c) 8
d) 9

Answer 1

See, if the interior angle is 135, then the exterior is 180 - 135 = 45.
We know that the exterior angles in a polygon add up to 180.
So, number of sides = \(\Large \color{purple}{\rightarrow {180 \over 45} = 4 }\)

Answer 2

Perhaps the sum of the exterior angles of a polygon add up to 360 since we have to go all the way around the circle.

Answer 3

360 I meant :P I got it wrong

Answer 4

\(\Large \color{purple}{\rightarrow {360 \over 45} = 8 }\)

Answer 5

8 sides actually

Answer 6

\[135=\frac{(n-2)(180)}{n}\]
\[135n=180n-360\]
\[-45n=-360\]
\[n=8\]