SSC CGL 3 Sep 2016 Paper

Question : 61 of 100

Marks: +1, -0

Three consecutive angles of a cyclic quadrilateral are in the ratio of 1 : 4 : 5. The measure of fourth angle is :

120°
60°
30°
80°

Solution:

The sum of the opposite angles of a cyclic quadrilateral is 180°.
For a quadrilateral ABCD,
∠A = x°; ∠B = 4x°; ∠C = 5x°
∴ x + 5x = 180° ⇒ 6x = 180°
⇒ x =

{180°}/4

= 30°
∴ ∠B + ∠D = 180°
⇒ 4 × 30° + ∠D = 180°
⇒ ∠D = 180° - 120° = 60°

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