Question

three angles of a seven sided polygon are 132 degrees each and the remaining four angles are equal . find the value of each angle?

Answer 1

The sum of interior angles of a polygon = (2n-4)90 Where 'n' is the no. of sides

For this polygon sum of angles = (2x7-4)x90= 900 degree

3 angles = 3 x 132 = 396
Remaining 4 angles = 900 - 396 = 504 degrees
Each of the 4 angles = 504/4 = 126 degrees

Answer 2

Solution:-

The sum of interior angles of a polygon having n number of sides is given by (n - 2)*180
Sum of the interior angles of the seven side polygon = (7 - 2)*180
= 900°
The three angles of the seven sided polygon are 132° each.
Since the remaining 4 angles are equal.
Let each of these angles be 'x'
Then 132 + 132 + 132 + x + x + x + x = 900°
⇒ 396 + 4x = 900°
⇒ 4x = 900 - 396
⇒ 4x = 504
⇒ x = 504/4
⇒ x = 126°
So, the value of each of the remaining four angles is 126°
Answer.