Question

In the adjoining figure, it is given that $\angle A={60}^{\circ }$, CE || 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

${55}^{\circ }$

$\angle ACE=\angle BAC={60}^{\circ }$
[$\because$Alternate angles]

$\angle ACB+\angle ACE+\angle ECD={180}^{\circ }$
[$\because$Angle on a straight line]

$\Rightarrow \angle ACB={180}^{\circ }-\angle ACE-\angle ECD={180}^{\circ }-{60}^{\circ }-{65}^{\circ }={55}^{\circ }$

$\therefore \angle ACB={55}^{\circ }$