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In a DeltaABC,BEbotAC,angleEBC=40^(@)and...

In a `DeltaABC,BEbotAC,angleEBC=40^(@)andangleCAD=30^(@)."If "angleACD=x^(@)andangleADB=y^(@)` find the values of x and y.

A

x=80 and y=50

B

x=50 and y=70

C

x=50 and y=80

D

x=70 and y=80

Text Solution

Verified by Experts

The correct Answer is:
C
We know that the sum of the angles of a triangle is `180^(@)`.
In `DeltaBCE` we have
`angleCBE+angleBEC+angleECB=180^(@)`
`:.40^(@)+90^(@)+x^(@)=180^(@)impliesx=50`.
Now, in `angleACD`, the side CD has been produced to B.
`:.ext.angleBDE=angleDAC+angleACD`
`impliesy^(@)=30^(@)+x^(@)impliesy=(30+50)=80`. Hence, x=50 and y=80.
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