Question

Q8. In figure, if lines PQ and RS intersects at a point T, such that ZPRT = 40°, ZRPT
= 95º and ZTSQ = 75°, find ZSQT.
(3)
P
950
400
es
T
R
75°​

Answer 1

In PRT

By angle sum property of triangle

∠PRT+∠RPT+∠PTR=180∘

⇒90∘+45∘+∠PTR=180∘

⇒135∘+∠PTR=180∘

⇒∠PTR=180∘−135∘

⇒∠PTR=45∘.

Also,

∠STQ=∠PTR

∠STQ=45∘ (vertically opposite angles)

In ΔSQT

By angle sum property of triangle 

∠SQT+∠STQ+∠TSQ=180∘

∠SQT+75∘+45∘=180∘

∠SQT+120∘=180∘

∠SQT=180∘−120∘

∠SQT=60∘

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Answer 2

Answer:

In PRT

By angle sum property of triangle

∠PRT+∠RPT+∠PTR=180

∘

⇒90

∘

+45

∘

+∠PTR=180

∘

⇒135

∘

+∠PTR=180

∘

⇒∠PTR=180

∘

−135

∘

⇒∠PTR=45

∘

.

Also,

∠STQ=∠PTR

∠STQ=45

∘

(vertically opposite angles)

In ΔSQT

By angle sum property of triangle

∠SQT+∠STQ+∠TSQ=180

∘

∠SQT+75

∘

+45

∘

=180

∘

∠SQT+120

∘

=180

∘

∠SQT=180

∘

−120

∘

∠SQT=60

∘