Question

In the adjoining figure it is given that $\angle A={60}^{\circ }CE\parallel BA$ AND $\angle ECD={65}^{\circ }$ then $\angle ACB=$ ______

• A. ${60}^{\circ }$
• B. ${55}^{\circ }$
• C. ${70}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${55}^{\circ }$

Given $BA||CE$ and $BD$ is transversal.

$\therefore \angle ABC=\angle ECD$ (Corresponding angles)

$\Rightarrow \angle ABC={65}^{\circ }$

Now using angle sum property in $△ABC$

$\Rightarrow \angle ACB+\angle CAB+\angle ABC={180}^{\circ }$

$\angle ACB+{60}^{\circ }+{65}^{\circ }={180}^{\circ }\Rightarrow \angle ACB={180}^{\circ }-{125}^{\circ }=55^{\circ }$