In the fig. below, if AB || CD, ∠ APQ = 50 ∘ and ∠ PRD = 127 ∘ , find x and y. Options: A . &nbsp 50 ∘ , 67 ∘ B . &nbsp 50 ∘ , 77 ∘ C . &nbsp 77 ∘ , 87 ∘ D . &nbsp 77 ∘ , 97 ∘

Answer: Option B : B Since AB || CD ∠ APQ = ∠ PQR (Alternate interior angles of transversal PQ) ⇒x = 50 ∘ ∠ APR = ∠ PRD (Alternate interior angles of transversal PR) ⇒y + 50 ∘ = 127 ∘ ⇒ y = 127 ∘ - 50 ∘ = 77 ∘

In the fig. below, if AB || CD, ∠APQ = 50∘ and ∠PRD = 127∘, find x and

Question

In the fig. below, if AB || CD, $∠$ APQ = 50 $^{\circ}$ and $∠$ PRD = 127 $^{\circ}$ , find x and y.

Options:

A . 50

^{\circ}

, 67

^{\circ}

B . 50

^{\circ}

, 77

^{\circ}

C . 77

^{\circ}

, 87

^{\circ}

D . 77

^{\circ}

, 97

^{\circ}

Answer: Option B
:
B

Since AB || CD

∠APQ = ∠PQR (Alternate interior angles of transversal PQ)

⇒x = 50 $^{\circ}$

∠APR = ∠PRD (Alternate interior angles of transversal PR)

⇒y + 50 $^{\circ}$ = 127 $^{\circ}$

⇒ y = 127 $^{\circ}$ - 50 $^{\circ}$

= 77 $^{\circ}$

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