In the figure below- if AB - CD- -APQ - 50- and -PRD - 127- find x and y-

Since AB || CD, ∠APQ = ∠PQR (Alternate interior angles of transversal PQ) ⇒ x = 50^∘ ∠APR = ∠PRD (Alternate interior angles of transversal PR) ⇒ y + 50^∘ ...

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Standard VII

Mathematics

Vertically Opposite Angles

In the figure...

Question

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

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Solution

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 $^{\circ}$

⇒ y = 77 $^{\circ}$

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

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∘ ⇒ y = 77∘

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

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 $^{\circ}$

⇒ y = 77 $^{\circ}$