The interior angles of a quadrilateral are (x + 15)o, (2x – 45)o and (x…

The interior angles of a quadrilateral are (x + 15)^o, (2x – 45)^o and (x + 10)^o. Find the value of the least interior angle.

Correct Answer: Option D

Explanation

(x + 15)^o + (2x – 45)^o + (x + 10)^o = (2n – 4)90^o
when n = 4
x + 15^o + 2x – 45^o + x – 30^o + x + 10^o = (2 x 4 – 4) 90^o
5x – 50^o = (8 – 4)90^o
5x – 50^o = 4 x 90^o = 360^o
5x = 360^o + 50^o
5x = 410^o
x = (frac{410^o}{5})
= 82^o
Hence, the value of the least interior angle is (x – 30^o)
= (82 – 30)^o
= 52^o