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Find the value of x and y in the following figure.

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x = 30^{\circ}, y = 50^{\circ}

x = 30^{\circ}, y = 10^{\circ}

x = 10^{\circ}, y = 50^{\circ}

x = 20^{\circ}, y = 30^{\circ}

answer is A.

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Detailed Solution

Given:

∠ P

40^{\circ}

∠ S

90^{\circ}

∠ R

=y
In

Δ

PSR

∠ P + ∠ S + ∠ R = 180^{\circ}

[

∵

Property sum of angle of triangle]
By putting the given value,

∠ P + ∠ S + ∠ R = 180^{\circ}

\Rightarrow 40^{\circ} + 90^{\circ} + y = 180^{\circ}

\Rightarrow 130^{\circ} + y = 180^{\circ}

\Rightarrow y = 180^{\circ} - 130^{\circ}

\Rightarrow y = 50^{0}

Similarly, In

Δ

PSQ

∠ P + ∠ S + ∠ Q = 180^{\circ}

By putting the value

{∠ Q = 60}^{\circ}

∠ P = x

∠ S

90^{\circ}

∴ ∠ P + ∠ S + ∠ Q = 180^{0}

\Rightarrow 60^{\circ} + 90^{\circ} + x

= 180^{\circ}

\Rightarrow 150^{\circ} + x = 180^{\circ}

\Rightarrow x = 180^{\circ} - 150^{\circ}

\Rightarrow x = 30^{\circ}

so, value of x =

30^{\circ}

and y =

50^{\circ}

Correct option is 1.

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