The interior angles of a quadrilateral are (x + 15)°, (2x – 45)°, ( x – 30)° and (x + 10)°. Find the value of the least interior angle.
- 112o
- 102o
- 82o
-
52o
The correct answer is: D
Explanation
(x + 15)o + (2x - 45)o + (x + 10)o = (2n - 4)90o
when n = 4
x + 15o + 2x - 45o + x - 30o + x + 10o = (2 x 4 - 4) 90o
5x - 50o = (8 - 4)90o
5x - 50o = 4 x 90o = 360o
5x = 360o + 50o
5x = 410o
x = \(\frac{410^o}{5}\)
= 82o
Hence, the value of the least interior angle is (x - 30o)
= (82 - 30)o
= 52o
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