Question

In the following figure, sides QP and RQ of triangle PQR are produced to points S and T respectively. If angle SPR=135° and angle PQT=110° , find angle PRQ​

Answer 1

Answer:

65°

Step-by-step explanation:

first QR=180°-110°=70° (ACCORDING TO LINEAR PAIR)

NOW PQR+PRQ=SPR. ( ACCORDING TO EXTERIOR ANGLE PROPERTY)

SO. 70°+PRQ=135°

PRQ = 135°-70°=65°

Answer 2

GIVEN:-

$\large\sf{\angle{SPR}=135°}$

$\large\sf{\angle{PQT} =110°}$

TO FIND:-

$\large\sf{\angle{PRQ}}$

PROOF:-

$\implies$$\large\sf{\angle{PQT}+\angle{SQR}=180°}$

$\implies$$\large\sf{110°+\angle{SQR}=180°}$

$\implies$$\large\sf{\angle{SQR}=180°-110°}$

$\implies$$\large\sf{\angle{SQR}=70°}$

━━━━━━━━━━━━━━━

$\implies$$\large\sf{\angle{SPR}+\angle{RPQ}=180°}$

$\implies$$\large\sf{135°+\angle{RPQ}=180°}$

$\implies$$\large\sf{\angle{RPQ}=180°-135°}$

$\implies$$\large\sf{\angle{RPQ}=45°}$

━━━━━━━━━━━━━━━

$\implies$$\large\sf{\angle{PRQ}+\angle{SQR}+\angle{RPQ}=180°}$

$\implies$$\large\sf{\angle{PRQ}+70°+45°=180°}$

$\implies$$\large\sf{\angle{PRQ}+115°=180°}$

$\implies$$\large\sf{\angle{PRQ}=180°-115°}$

$\implies$$\large\sf{\angle{PRQ}=65°}$