Question

A road sign is in the shape of a regular heptagon. What is the measure of each angle on the sign? Round to the nearest tenth.

128.6
900
64.3
231.4

Answer 1

Answer: Measure of each angle on the sign is 128.6° .

Explanation:

Since we have given that

A road sign is in the shape of a regular heptagon.

As we know that "Sum of exterior angles is always 360°":

And there is 7 sides in a regular heptagon.

So, Measure of each exterior angle is given by

`(360^\circ)/(7)\\\\=51.42^\circ`

so, we know that "Sum of exterior angle and interior angle is supplementary."

`Interior\ Angle+Exterior\ Angle=180^\circ\\\\Interior\ Angle+51.42^\circ=180^\circ\\\\Interior\ Angle=180^\circ-51.42^\circ\\\\Interior\ Angle=128.58^\circ=128.6^\circ`

Hence, Measure of each angle on the sign is 128.6° .

Answer 2

Answer
A) 〖128.6〗^o

Explanation
The question requires us to find the interior angle of a regular heptagon.
To do this first calculate the exterior angle of that polygon.
The sum of exterior angles is 360o. A heptagon has 7 sides.
So, one exterior angle = 〖360〗^o/7=〖51.4〗^o
interior angle+exterior angle=〖180〗^o
exterior=180-51.4=〖128.6〗^o