Question

In the figure, ACE, BCF and DCG are straight lines and AB || HC.

Find the angles p,q,r and s.

• A. $p={45}^{\circ },q={50}^{\circ },r={65}^{\circ },s={50}^{\circ }$
• B. $p={45}^{\circ },q={65}^{\circ },r={50}^{\circ },s={50}^{\circ }$
• C. $p={45}^{\circ },q={65}^{\circ },r={50}^{\circ },s={65}^{\circ }$
• D. $p={45}^{\circ },q={50}^{\circ },r={65}^{\circ },s={65}^{\circ }$

Answer 1

The correct option is A $p={45}^{\circ },q={50}^{\circ },r={65}^{\circ },s={50}^{\circ }$

In $\Delta ABC,r={180}^{\circ }-{50}^{\circ }-{65}^{\circ }={65}^{\circ }\left[\text{angle sum property of a triangle}\right]$

$HC||AB\Rightarrow q={50}^{\circ }\left[\text{Alternative angles}\right]$.

s = q [Vertically opposite angles]
Hence, $s={50}^{\circ }$

Since BCF is a straight line,
$(p+{20}^{\circ })+q+r={180}^{\circ }\Rightarrow p={45}^{\circ }$
$\therefore p={45}^{\circ },q={50}^{\circ },r={65}^{\circ }$ and $s={50}^{\circ }$ are the required values.