In a cyclic quadrilateral ABCD, $∠$ A : $∠$ C = 3 : 1 and $∠$ B : $∠$ D = 1 : 5; find each angle of the quadrilateral.

Open in App

Solution

$\angle A : \angle C = 3:1 \Rightarrow \angle A = 3x \ and \ \angle C = x$

$\angle A + \angle C = 180^o$ ( $ABCD$ is a cyclic quadrilateral)

$\therefore 3x + x = 180^o \Rightarrow x = 45^o$

$\therefore \angle A = 135^o \ and \ \angle C = 45^o$

Also given $\angle B:\angle D = 1:5 \Rightarrow \angle B = y \ and \ \angle D = 5y$

$\angle B + \angle D = 180^o$ ( $ABCD$ is a cyclic quadrilateral)

$\therefore y + 5y = 180^o \Rightarrow y = 30^o$

$\therefore \angle B = 30^o \ and \ \angle D = 150^o$

$\\$

Suggest Corrections

Similar questions

A B C D

∠ = {(2 x + 4)}^{o}

∠ B = {(y + 3)}^{o}, ∠ C = {(2 y + 10)}^{o}

∠ D = {(4 x - 5)}^{o}

A B C D

∠ A = (2 x + 4), ∠ B = (y + 3), ∠ C = (2 y + 10), ∠ D = (4 x - 5)

∠ A = (2 x + 4)^{o}, ∠ B = {(y + 3)}^{o}, ∠ C = {(2 y + 10)}^{o} a n d ∠ D = {(4 x - 5)}^{o} .

Join BYJU'S Learning Program