PQR is a triangle in which PQ = PR. QR is produced to point S. T is a point on PR and U is a point outside the triangle. TU is parallel to PQ and PU is parallel to QR. If angle ∠PQR = 70° and ∠PUS = 150°, find the value of ∠USR.?

25°
35°
40°
30°

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 4 : 30°

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Since PQ = PR

∠PRQ = ∠PQR = 70°

⇒ ∠QPR = 180 - 70 - 70 = 40°

And ∠TRS = 180 - 70 = 110°

In the figure, UT which is parallel to PQ is extended till V

⇒ UV is parallel to PQ

⇒ ∠VTR = ∠QPR = 40°

Thus ∠UTR = 180 - ∠VTR = 180 - 40 = 140°

Since PU is parallel to QR

⇒ ∠PUV = ∠PQR = 70°

Given that ∠PUS = 150°

⇒ ∠TUS = 150 - 70 = 80°

In quadrilateral TUSR

⇒ ∠USR = 360 - ∠TRS - ∠TUS - ∠UTR

∴ ∠USR = 360 - 110 - 80 - 140 = 30°

4 views Answered 2022-09-04 04:29

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