Question

Three of exterior angle of n-sided polygon are 50° each two of it's interior angle are 127° and 135° and the remaining interior angle are 173 each .Find the value of n

Answer 1

Answer:

The value of n is 21.

Step-by-step explanation:

We are given that three of the exterior angle of the n-sided polygon are 50° each two of its interior angle are 127° and 135° and the remaining interior angle are 173 each.

As we know that the sum of all exterior angles of the polygon is 360°. Also, the number of remaining interior angles will be (n - 5).

And, the exterior angle = 180° - the interior angle.

So, according to the question;

$(3 \times 50) + (180-127) + (180 - 135) + (n - 5)\times (180-173) =360$

150 + 53 + 45 + 7(n - 5) = 360

248 + 7n - 35 = 360

213 + 7n = 360

7n = 360 - 213

7n = 147

n = $\frac{147}{7}$

n = 21

Hence, the value of n is 21 and this is a 21-sided polygon.