Question

$\text{In the given figure, the sides CB and BA of}\Delta ABC\text{hs been produced to D and E respectively such that}\angle ABD={110}^{\circ }and\angle CAE={135}^{\circ }.Then,\angle ACB=?$

$\left(a\right){65}^{\circ }\left(b\right){45}^{\circ }\left(c\right){55}^{\circ }\left(d\right){35}^{\circ }$

Answer 1

ANSWER:
(a) ${65}^{\circ }$
We have :
$\angle ABD+\angle ABC={180}^{\circ }\because CBDisastraightline\Rightarrow {100}^{\circ }+\angle ABC={180}^{\circ }\Rightarrow \angle ABC={70}^{\circ }$
Side AB of triangle ABC is produced to E.
∴ $\angle CAE=\angle ABC+\angle ACB\Rightarrow {135}^{\circ }={70}^{\circ }+\angle ACB\Rightarrow \angle ACB={65}^{\circ }$