Question

In the figure ,PQ||MN||SR,PS||MU||NR,and angle UVQ=120°.Find the measure of angle PSU and angle URQ
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Answer 1

Answer:

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

∘