Question

In the given figure, $PQ,RS$ and $UT$ are parallel lines. If $c={75}^{\circ }$ and $a=\left(2.5\right)c$, find $b+d/2$.

• A. ${92}^{\circ }$
• B. ${115}^{\circ }$
• C. ${112.5}^{\circ }$
• D. ${135.5}^{\circ }$

Answer 1

The correct option is C ${112.5}^{\circ }$

We have, $c={75}^{\circ }$
$\therefore a=\frac{2}{5}c=\frac{2}{5}\times {75}^{\circ }={30}^{\circ }$
Now, $UT\parallel PQ$
$\Rightarrow c=a+b$ (Alternate angles)
$\Rightarrow {75}^{\circ }={30}^{\circ }+b\Rightarrow b={75}^{\circ }-{30}^{\circ }={45}^{\circ }$
Also, $PQ\parallel RS$
$\therefore b+d={180}^{\circ }$ (Co-interior angles)
$\Rightarrow d={180}^{\circ }-{45}^{\circ }={135}^{\circ }$
So, $b+\frac{d}{2}={45}^{\circ }+\frac{{135}^{\circ }}{2}={45}^{\circ }+{67.5}^{\circ }={112.5}^{\circ }$.