PQRS is a cyclic quadrilateral $∠ P = 3 x, ∠ Q = y, ∠ R = x, ∠ S = 5 y$ . Find x and y.

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Solution

Since, PQRS is a cyclic quadrilateral.

So,
$\begin{matrix} 5 y + y = 180 & and, & 3 x + x = 180 6 y = 180 & 4 x = 180 y = 30^{\circ} & x = \frac{180}{4} x = 45^{\circ} \end{matrix}$

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Similar questions

PQRS is a cyclic quadrilateral $∠ P = 3 x, ∠ Q = y, ∠ R = x, ∠ S = 5 y$ . Find x and y.

∠ Q = ∠ R = 65^{\circ},

∠ P

∠ S

P Q R S

∠ P = 3 x + 20^{\circ},

∠ Q = 4 x + 10^{\circ},

∠ R = 4 y - 30^{\circ}

∠ S = 2 y .

(x - y)

∠ P - ∠ R = 30^{o}

∠ Q - ∠ S = - 30^{o}

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