Question

In the figure, AO and CD are parallel to YZ. Find the value of x.

• A. 40°
• B. 45°
• C. 60°
• D. 65°

Answer 1

The correct option is C 60°

Given, CD || YZ,
$\angle CBY=\angle BCD$
(Alternate interior angles)

$\Rightarrow \angle CBY=130°$

$\Rightarrow$ $\angle ABY=130°-x$

Similarly, AO || YZ,
$\angle ABZ=\angle BAO$
(Alternate interior angles)

$\angle ABZ=110°$

$\Rightarrow$ $\angle CBZ=110°-x$

$\angle ABY+x+\angle CBZ=180°\text{(Linear pair)}$

$(130°-x)+x+(110°-x)=180°$

$240°-x=180°$
$x=60°$

Hence, the value of $x$ is 60°.