2010
Mathematics
JAMB
The interior angles of a quadrilateral are (x + 15)°, (2x - 45)°, ( x - 30)° and (x + 10)°. Find the value of the least interior angle.
A.
112°
B.
102°
C.
82°
D.
52°
Correct Answer: 52°
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 - 50° = (8 - 4)90° 5x - 50° = 4 x 90° = 360° 5x = 360° + 50° 5x = 410° x = 410°/5 = 82° Hence, the value of the least interior angle is (x - 30°) = (82 - 30)° = 52°
(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 - 50° = (8 - 4)90° 5x - 50° = 4 x 90° = 360° 5x = 360° + 50° 5x = 410° x = 410°/5 = 82° Hence, the value of the least interior angle is (x - 30°) = (82 - 30)° = 52°THIS WEEK's
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