Question

In the given figure, anglePQT = angleTRS and angleTQS = angleTRP. If angleRPQ =180º and angleRSQ = 120°, then
find the value of angleRTQ.​

Answer 1

Answer:

answers is 150°

Step-by-step explanation:

In triangle PQR

angle P + angle Q + angle R =180°

180°+Q+R= 180°

Q+R=0°

let angle TQS and angle TRP be y

and angle TQP and angle TRS be z

now when angle Q and angle R are equal to 0

hence Q=R

y+z+angle SQR=y+z+angleSRQ

HENCE angle SQR=angle SRQ

In ∆SQR

angle QSR+ angle SQR+ angle SRQ=180°

120°+angleSQR+angleSRQ=180°

2 angleSRQ=60°

angleSRQ=30°

Now anglePQR=0°

y+z+30°=0°

y+z=-30°

In ∆ TQR

angleQTR+angleTQR+angleTRQ=180°

angleQTR+(y+30°)+(z+30°)=180°

angleQTR+y+z+60°=180°

angleQTR+(-30°)=120°

angleQTR=120°+30°

angleQTR=150°

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