in the figure given below, angle SQR=28°, angle QRT=65° if PQ PS, PQ ST, then find the value of x and y
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Answer:
x = 180° - 143° = 37°
Explanation:
In △QSR, we have
∠QRT=∠RSQ+∠SQR ....(Exterior angle of triangle is equal t sum of interior opposite angles)
⇒65
∘
=∠RSQ+28
∘
⇒∠RSQ=65
∘
−28
∘
⇒∠RSQ=37
∘
We have y
∘
+∠RSQ=90
∘
....(Given)
⇒y+37
∘
=90
∘
⇒y=90
∘
−37
∘
=53
∘
In △PQS, we have
x
∘
+y
∘
+∠P=180
∘
....(Angle sum property)
⇒x+53
∘
+90
∘
=180
∘
⇒x=180
∘
−143
∘
=37
∘
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