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In the given figure, two rays BD and CE ...

In the given figure, two rays `BD` and `CE` intersect at a point `A.` The side `BC` of `DeltaABC` have been produced on both sides to points `F` and `G` respectively. If `angleABF=x^(@),angleACG=y^(@)andangleDAE=z^(@)" then "z=?`

A

`x+y-180`

B

`x+y+180`

C

`180-(x+y)`

D

`x+y+360^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A
`angleBAC=angleEAD=z^(@),angleABC=(180^(@)-x^(@)),angleBCA=(180^(@)-y^(@))`,
`angleBAC+angleABC+angleBCA=180^(@)`
`impliesz+(180-x)+(180-y)=180impliesz=(x+y)-180^(@)`.
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