Question

176 Maths Mileage Q6. Find the value of the variables , y, z in the following figures. (ii) P () 70 40 25 60 M (PO I LM)​

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>>Quadrilaterals and Their Various Types

>>In Fig. 6.43, if PQ PS, PQ∥ SR, SQR = 2

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In Fig. 6.43, if PQ⊥PS,PQ∥SR,∠SQR=28

0

and ∠QRT=65

0

, then find the values of x and y.

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Solution

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Given, PQ⊥PS,PQ∥SR,∠SQR=28

∘

,∠QRT=65

∘

According to the question,

x+∠SQR=∠QRT (Alternate angles as QR is transversal.)

⇒x+28

∘

=65

∘

⇒x=37

∘

Also ∠QSR=x

⇒∠QSR=37

∘

Also ∠QRS+∠QRT=180

∘

(Linear pair)

⇒∠QRS+65

∘

=180

∘

⇒∠QRS=115

∘

Now, ∠P+∠Q+∠R+∠S=360

∘

(Sum of the angles in a quadrilateral.)

⇒90

∘

+65

∘

+115

∘

+∠S=360

∘

⇒270

∘

+y+∠QSR=360

∘

⇒270

∘

+y+37

∘

=360

∘

⇒307

∘

+y=360

∘

⇒y=53

∘