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Question
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
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Solution
Angles of quadrilateral are,
(4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°
∴ 4x + 5(x + 2) + (7x - 20) + 6(x + 3) = 360°
4x + 5x + 10 + 7x - 20 + 6x + 18 = 360°
22x + 8 = 360°
22x = 360° - 8°
22x = 352°
x = 16°
Hence angles are,
(4x)° = (4 × 16)° = 64°
5(x + 2)° = 5(16 + 2)° = 90°
(7x - 20)° = (7 × 16 - 20)° = 92°
6(x + 3)° = 6(16 + 3) = 114°
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