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In the given figure, PQRS is an isoscele...


In the given figure, PQRS is an isosceles trapezium and `bar(PQ)||bar(SR)||bar(MN)` If `/_ SPM=70^(@)` and `/_ PQR =110^(@)`, then find `/_ PMN.`

A

`140^(@)`

B

`150^(@)`

C

`120^(@)`

D

`100^(@)`

Text Solution

Verified by Experts

The correct Answer is:
a

Given that PQRS is an isosceles trapezium,
`bar(PQ) ||bar(SR)||bar(MN)`
`/_ SPM =70^(@) ` and `/_ PQR =110^(@)` ( given )
`implies /_ PQR = /_ SPQ =110^(@)`
`/_ MPQ = /_ SPQ - /_ SPM =110^(@) -70^(@) = 40^(@)`
`bar(PQ )||bar(MN) implies /_ PMN =180^(@) -/_ MPQ `
`=180^(@) - 40^(@) =140^(@)`
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