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;
[tex](3 \times 50) + (180-127) + (180 - 135) + (n - 5)\times (180-173) =360[/tex]
150 + 53 + 45 + 7(n - 5) = 360
248 + 7n - 35 = 360
213 + 7n = 360
7n = 360 - 213
7n = 147
n = [tex]\frac{147}{7}[/tex]
n = 21
Hence, the value of n is 21 and this is a 21-sided polygon.
