Question

One angle of a heptagon is 132 degree and all the other angles are equal then find the measure of each of the angles

Answer 1

Given,

The polygon is a heptagon.

One internal angle is = 132°

Remaining angles are equal.

To find,

The measurement of the remaining angles of the given heptagon.

Solution,

First of all, we need to calculate the sum of the internal angles of the heptagon by the already available mathematical formula.

The mathematical formula is,

Sum of the internal angles of a polygon = 180° × (n-2)

[Here, n = number of sides of a polygon]

So, the sum of the internal angles of a heptagon will be = 180° × (7-2) = 900° ....(1)

Let,the other remaining angles = x°

[Assume, x as a variable to do the further mathematical calculations.]

Sum of the equal 6 angles = 6 × x° = 6x°

Sum of the all 7 angles = 132° + 6x° .....(2)

Now,if we compare (1) and (2),we will get that,

132 + 6x = 900

6x = 768

x = 128

Hence,the measure of the each equal angle is 128°.