The values of x and y in the given figure are respectively ___.

$25^{\circ}$ and $60^{\circ}$

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$40^{\circ}$ and $60^{\circ}$

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$60^{\circ}$ and $25^{\circ}$

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$40^{\circ}$ and $25^{\circ}$

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Solution

The correct option is D
$40^{\circ}$ and $25^{\circ}$

$∠ A + ∠ C = 180^{\circ}$ [Sum of opposite angles of a cyclic quadrilateral is $180^{\circ}$ ]
$\Rightarrow 2 x + 4 + 4 y - 4 = 180^{\circ}$
$\Rightarrow 2 x + 4 y = 180^{\circ}$
$\Rightarrow x + 2 y = 90^{\circ}$ .... (i)

$∠ B + ∠ D = 180^{\circ}$ [Sum of opposite angles of a cyclic quadrilateral is $180^{\circ}$ ]
$\Rightarrow x + 10 + 5 y + 5 = 180^{\circ}$
$\Rightarrow x + 5 y = 165^{\circ}$ .... (ii)

On substracting (i) from (ii), we get
$3 y = 75 \Rightarrow y = 25^{\circ}$
Also, $x = 40^{\circ}$

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Similar questions

x

y

In the given figure, $∠ A = 60^{\circ}$ and $∠ A B C = 80^{\circ}$ , then $∠ D P C$ and $∠ B Q C$ are respectively ___.

∠ 1 = 2 y + 25^{\circ}, ∠ 2 = x + 15^{\circ}

x

y

2 y + 25^{\circ} = 3 y

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$

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