Management Aptitude Test 2016 Paper

Question : 116 of 200

Marks: +1, -0

In a cyclic quadrilateral ABCD, angle A is double than its opposite angle and the difference between the other two angles is one-third of angle A. The maximum difference between any two angles of this quadrilateral is _______ .

30°
10°
20°
60°

Validate

Solution:

(d ) Let the angle C be x.
Then, ∠A = 2x
Also. ∠B - ∠D =

{2x}/3

We know that opposite angles of a cyclic quadrilateral are supplementary
i.e. ∠A + ∠C = 180°
⇒ 2x + x = 180°
⇒ 3x = 180°
⇒ x = 60°
∴ ∠A = 2x = 120°
and ∠B - ∠D =

120°/3

= 40 .......(i)
Also, ∠B + ∠D =180° ..........(ii)
On solving Eqs (i) and (ii). we get
∠D = 70° and ∠B = 110°
∴ Maximum difference = 120° - 60° = 60°

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