Question

In figure, if $AB\parallel CD$, then find the value of $\angle GHS$

• A. ${148}^o$
• B. ${138}^o$
• C. ${118}^o$
• D. ${108}^o$

Answer 1

The correct option is D ${108}^o$

In the figure, $AB\parallel CD$

$\angle PRB=2x$ ....... (Given)

As lines $AB$ and $PQ$ intersect at $R$

$\angle PRB=\angle GRS$

$⟹\angle GRS=2x$

Also, $AB\parallel CD$

$\angle GRS+\angle HSR={180}^o$ ...... (Sum of interior angle is supplementary)

$\angle HSR=3x$ ....... (Given)

$⟹2x+3x={180}^o$

$⟹5x=\frac{{180}^o}{5}$

$⟹x={36}^o$

$\angle EGA=2x$ ........ (Given)

$\angle EGA+\angle EGR={180}^o$

$⟹2x+\angle EGR={180}^o$

$⟹\angle EGR={180}^o-2x$

$Also\angle GHS=\angle EGR$ ....... (Corresponding angles are equal)

$⟹\angle GHS={180}^o-2x$

Putting value of $x={36}^o$

$\angle GHS={180}^o-2\times 36={180}^o-{72}^o={108}^o$

$⟹\angle GHS={108}^o$