Question 124

The three successive angles of a cyclic quadrilateral are in the ratio 1:3:4, find the measure of the fourth angle ?

Solution

Let the angles be $$x,3x$$ and $$4x$$ respectively.

Sum of opposite angles in a cyclic quadrilateral = $$180^\circ$$

=> $$x+4x=5x=180^\circ$$

=> $$x=\frac{180}{5}=36^\circ$$

=> 2nd angle = $$3\times36=108^\circ$$

$$\therefore$$ 4th angle (opposite 2nd angle) = $$180^\circ-108^\circ=72^\circ$$

=> Ans - (B)

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