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In a angle PQR, M lies on PR and between...

In a `angle PQR`, M lies on PR and between P and R such that `QR=QM=PM`. If `angle MQR=40^@`, then find `angle P`.

A

`35^@`

B

`25^@`

C

`45^@`

D

`55^@`

Text Solution

Verified by Experts

The correct Answer is:
A

Given `QR=QM=PM and angle MQR =40^@`
In `Delta QMR , QM =QR`
`therefore angle QRM =angle QMR`
Now, `angle QRM =angle QMR`
`=(1)/(2)(180^@-40^@)=70^@`
In `Delta MPQ, PM=MQ`
`angle PQM =angle MPQ (1)`
But `angle +angle MPQ=angle QMR=70^@ (2)`
form Eqs. (1) and (2)
`angle MPQ =(1)/(2)(70^@)=35^@`
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