Question

In the adjoining figure, it is given that $\angle A={60}^{},$ $CE\parallel BA$ and $\angle ECD={65}^{}.$ Then $\angle ACB$ equals.

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

Answer 1

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

R.E.F. Image.

$\angle A={60}^{\circ }$

CE || AB

$\angle ECD={65}^{\circ }$

(Interior Alternate Angle)

$\angle BAC=\angle ACE$

$\angle ACE={60}^{\circ }$

$\angle BCD={180}^{\circ }$ (linear Angle) or (linear Point)

$\angle ACB+\angle ACE+\angle ECD={180}^{\circ }$

$\angle ACB={180}^{\circ }-(60+65)$

$={180}^{\circ }-\left(125\right)$

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