In the given figure- if nbsp- BCA - - RPQ - 15- then - PQR is - 45-15-55- nbsp-35-

The correct option is A 45^∘ In Δ ABC and Δ PQR, ∠ BCA = ∠ RPQ = 15^∘ .... (Given) BC = PR = 1 km ....... nbsp;(Given) AC = PQ = 1.3 km .... nbsp;(Gi ...

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Byju's Answer

Standard VIII

Mathematics

SAS Congruency Postulate

In the given ...

Question

In the given figure, if $∠ B C A = ∠ R P Q = 15^{\circ},$
then $∠ P Q R$ is ______.

$45^{\circ}$

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$35^{\circ}$

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$15^{\circ}$

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$55^{\circ}$

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Solution

The correct option is A
$45^{\circ}$

In $Δ A B C$ and $Δ P Q R$ ,

$∠ B C A = ∠ R P Q$ = $15^{\circ}$ .... (Given)

$B C = P R = 1 k m$ ....... (Given)

$A C = P Q = 1.3 k m$ .... (Given)

Thus, $Δ A C B ≅ Δ Q P R$ by SAS congruency.
$\Rightarrow ∠ P Q R = ∠ B A C$ .... (CPCT)

Along the horizontal line through point A, we have
$90^{\circ} + ∠ B A C + 45^{\circ} = 180^{\circ}$
$∠ B A C = 180^{\circ} - 45^{\circ} - 90^{\circ}$
$\Rightarrow ∠ P Q R = ∠ B A C = 45^{\circ}$

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In the given figure, if ∠BCA=∠RPQ=15∘, then ∠PQR is ______.

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