Question

From the figure below, AA' is parallel to CC'. Given, $\angle w=135°$ and $\angle z=147°$. Find the value of $\angle x$.

• A. 78°
• B. 85°
• C. 118°
• D. 123°

Answer 1

The correct option is A 78°

Given,
$\angle w=135°$
$\angle z=147°$

Construction: Draw a line parallel to AA' and CC'. Let the line be be BB'.

$\angle ABC=\angle AB{B}^{\prime }+\angle CB{B}^{\prime }$

$\angle AB{B}^{\prime }=\angle w^{\prime }$ .... (Alternate interior angles)

$\angle CB{B}^{\prime }=\angle z^{\prime }$ ..... (Alternate interior angles)

$\angle w+\angle w^{\prime }=180°$ .... (Linear Pair)
$w^{\prime }=180°-w=180°-135°=45°$

$\angle z+\angle z^{\prime }=180°$ ..... (Linear Pair)
$z^{\prime }=180°-z=180°-147°=33°$

Substitute $\angle AB{B}^{\prime }$ by $w^{\prime }$ and $\angle CB{B}^{\prime }$ by $z^{\prime }$.
$\Rightarrow \angle ABC=\angle AB{B}^{\prime }+\angle CB{B}^{\prime }$
$\Rightarrow \angle ABC=w^{\prime }+z^{\prime }=45°+33°=78°$