Question

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^(@)`

Answer 1

Correct Answer - 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^(@)`