Question

In the given figure ab||CD angle bpr =70 and angle pqc =120 find x and y

Answer 1

Here is your solution.

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Answer 2

Answer: The value of x is 110°.

              The value of y is 10°.

Step-by-step explanation:

Given:In the given figure ab||CD ∠$BPR$ =70° and ∠$P Q C$ =120°

To find:We have to find the value of x and y.

Explanation:

Step 1:∠$PQC$ and ∠$PQR$ is linear pair angles because they are formed in a straight line.As we know that the sum of linear pair angles is 180°.

So,                         ∠$PQC$ + ∠$PQR$ $= 180$°

⇒                               $120$° $+$ ∠$PQR = 180$°

⇒                                          ∠$PQR = 180$° $- 120$°

⇒                                          ∠$PQR = 60$°

∴ The value of ∠$PQR$ is 60°.

Step 2:∠$BPR$ is exterior angle for Δ$PQR$ at vertex P.As we know that by exterior angle property of triangle that the measure of exterior angle is equal to the sum of the two opposite interior angles of the triangle.

So,                          ∠$PQR +$ ∠$y =$ ∠$BPR$

⇒                                $60$° $+$ ∠$y =$ $70$°  

⇒                                         ∠$y = 70$° $- 60$°

⇒                                         ∠$y = 10$°

∴ The value of y is 10°.

Step 3:∠$PQC$ is exterior angle for Δ$PQR$ at vertex P.As we know that by exterior angle property of triangle that the measure of exterior angle is equal to the sum of the two opposite interior angles of the triangle.

So,                                 ∠$x +$∠$y = 120$°

⇒                                 ∠$x+10$°$=$ $120$°

⇒                                         ∠$x = 120$°$-10$°

⇒                                         ∠$x =$ $110$°

∴  The value of x is 110°.

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