Question

In the figure given, if AB || CD, Find the values of 'p' and 'q'.

• A. ${75}^{\circ }$ and ${20}^{\circ }$
• B. ${20}^{\circ }$ and ${75}^{\circ }$
• C. ${25}^{\circ }$ and ${70}^{\circ }$
• D. ${70}^{\circ }$ and ${25}^{\circ }$

Answer 1

The correct option is D

${70}^{\circ }$ and ${25}^{\circ }$

The lines AB || CD.
$\therefore \angle EGB=\angle GHD\left[\text{Corresponding angles}\right]$
$\Rightarrow \angle GHD={65}^{\circ }$

$\Rightarrow \angle GHO+\angle OHD={65}^{\circ }$
$\Rightarrow q^{\circ }={65}^{\circ }-{40}^{\circ }={25}^{\circ }$

Draw a line XY through 'O' parallel to AB and CD.
Since XY || AB, $\angle XOG=\angle BGO$
$\Rightarrow XOG={45}^{\circ }$ (Alternate angles)
and $XY||CD\Rightarrow \angle XOH=\angle OHD$ (Alternate angles)
$\Rightarrow XOH={25}^{\circ }$

But $p^{\circ }=\angle XOG+\angle XOH$
$\Rightarrow p={45}^{\circ }+{25}^{\circ }={70}^{\circ }$
$\therefore p={70}^{\circ }$ and $q={25}^{\circ }$