In the given figure- if - BCA - RPQ -15- then - PQR isA- 45-B- 35-C- 15-D- 55-

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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Congruence of Triangles

In the given ...

Question

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

$45^{\circ}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$35^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$15^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$55^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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
$90^{\circ} + ∠ B A C + 45^{\circ} = 180^{\circ}$
$∠ B A C = 180^{\circ} - 45^{\circ} - 90^{\circ}$
$\Rightarrow ∠ P Q R = ∠ B A C = 45^{\circ}$

Suggest Corrections

Similar questions

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

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

In the given figure, $∠$ BCA = $∠$ RPQ = $15^{\circ}$ . Find $∠$ BAC is

In the given figure $∠ B C A$ = $∠ R P Q$ = $25^{\circ}$ , then find $∠ P Q R$ .

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

Join BYJU'S Learning Program

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

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