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In the figure, if AB CD, APQ={ 50 }^{ } and PRD={ 127 }^{ },

Question

In the figure, if $A B ∥ C D, ∠ A PQ = 50$ and $∠ PR D = 127$ , find $x$ and $y$ .

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Samuel Discussed

In the figure, if

A B ∥ C D, ∠ A PQ = 50

and

∠ PR D = 127

, find

x

and

y

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

Given,

A B ∥ C D, ∠ A PQ = 5 0^{\circ}, ∠ PR D = 12 7^{\circ}

According to the question

x = 5 0^{\circ}

(Alternate interior angles.)

∠ PR D + ∠ RPB = 18 0^{\circ}

(Angles on the same side of transversal.)

\Rightarrow 12 7^{\circ} + ∠ RPB = 18 0^{\circ}

\Rightarrow ∠ RPB = 5 3^{\circ}

Now,

y + 5 0^{\circ} + ∠ RPB = 18 0^{\circ}

(

A B

is a straight line.)

\Rightarrow y + 5 0^{\circ} + 5 3^{\circ} = 18 0^{\circ}

\Rightarrow y + 10 3^{\circ} = 18 0^{\circ}

\Rightarrow y = 7 7^{\circ}

∴ x = 5 0^{\circ}, y = 7 7^{\circ}

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Question Text	In the figure, if $A B ∥ C D, ∠ A PQ = 50$ and $∠ PR D = 127$ , find $x$ and $y$ .
Answer Type	Text solution:1
Upvotes	150