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The interior angles of a quadrilateral are (x + 15)o, (2x - 45)o and (x + 10)o. ...


Question

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.

Options

A) 112o

B) 102o

C) 82o

D) 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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Dicussion (1)

  • (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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