Question :
In the figure, in $ riangle {PQR}, {PT} \perp {QR}$ at ${T}$ and ${PS}$ is the bisector of $\angle {QPR}$. If $\angle {PQR}=78^{\circ}$, and $\angle {TPS}=24^{\circ}$, then the measure of $\angle {PRQ}$ is:

Option 1: 42$^{\circ}$
Option 2: 39$^{\circ}$
Option 3: 30$^{\circ}$
Option 4: 40$^{\circ}$

Question

Question :
In the figure, in $ riangle {PQR}, {PT} \perp {QR}$ at ${T}$ and ${PS}$ is the bisector of $\angle {QPR}$. If $\angle {PQR}=78^{\circ}$, and $\angle {TPS}=24^{\circ}$, then the measure of $\angle {PRQ}$ is:

Option 1: 42$^{\circ}$

Option 2: 39$^{\circ}$

Option 3: 30$^{\circ}$

Option 4: 40$^{\circ}$

Team Careers360 · Accepted Answer

Correct Answer: 30$^{\circ}$

Solution : In $ riangle$PQR, PT $ \perp$ QR at T and PS is the bisector of $\angle$QPR
$\angle$PQR = 78° and $\angle$TPS = 24°
In $ riangle$PQT,
$\angle$QPT = 180$^\circ$ – $\angle$PQR – $\angle$PTQ = 180$^\circ$ – 78$^\circ$ – 90$^\circ$ = 12$^\circ$
$\angle$SPQ = $\angle$QPT + $\angle$TPS = 12$^\circ$ + 24$^\circ$ = 36$^\circ$
Since PS is the bisector of $\angle$ QPR,
$\angle$QPR = 2 × $\angle$SPQ = 2 × 36$^\circ$ = 72$^\circ$
In $ riangle$PQR,
$\angle$ PRQ = 180$^\circ$ – $\angle$ PQR – $\angle$ QPR = 180$^\circ$ – 78$^\circ$ – 72$^\circ$ = 30$^\circ$
Hence, the correct answer is 30$^\circ$.

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Question : In the figure, in △PQR,PT⊥QR at T and PS is the bisector of ∠QPR. If ∠PQR=78∘, and ∠TPS=24∘, then the measure of ∠PRQ is: Option 1: 42∘Option 2: 39∘Option 3: 30∘Option 4: 40∘

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Question :
In the figure, in $△ P Q R, P T ⊥ Q R$ at $T$ and $P S$ is the bisector of $∠ Q P R$ . If $∠ P Q R = 78^{\circ}$ , and $∠ T P S = 24^{\circ}$ , then the measure of $∠ P R Q$ is:

Option 1: 42 $^{\circ}$
Option 2: 39 $^{\circ}$
Option 3: 30 $^{\circ}$
Option 4: 40 $^{\circ}$