In Fig , a+b= - Vidyadip

MCQ

In Fig , $a+b=$

A
$117^{\circ}$
B
$130^{\circ}$
C
$127^{\circ}$
D
$158^{\circ}$

✓

Answer

C. $127^{\circ}$
Since $A R B$ is a straight line.
$
\begin{array}{ll}
\therefore & \frac{x}{2}+5\left(\frac{x}{2}-1^{\circ}\right)+x+90^{\circ}=180^{\circ} \\
\Rightarrow & 4 x+4^{\circ}=180^{\circ} \Rightarrow 4 x=176^{\circ} \Rightarrow x=44^{\circ}
\end{array}
$
Using exterior angle property in $P Q R$, we obtain$
\begin{aligned}
& \angle Q R C=a+b \\
\Rightarrow \quad & \frac{x}{2}+5\left(\frac{x}{2}-1^{\circ}\right)=a+b \Rightarrow a+b=3 x-5^{\circ} \Rightarrow a+b=3 \times 44^{\circ}-5=127^{\circ}
\end{aligned}
$

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