Question

If four times an angle ${12}^0$ more than twice the difference between its supplement and its complement, then find the angle.

• A. ${38}^{\circ }$
• B. ${48}^{\circ }$
• C. ${42}^{\circ }$
• D. ${192}^{\circ }$

Answer 1

The correct option is B ${48}^{\circ }$

According to the question,
$4x={12}^{\circ }+2\left[\right({180}^{\circ }-x)-({90}^{\circ }-x\left)\right]$
$\Rightarrow 4x={12}^{\circ }+2[{180}^{\circ }-x-{90}^{\circ }+x]$
$\Rightarrow 4x={12}^{\circ }+2\times {90}^{\circ }$
$\Rightarrow 4x={192}^{\circ }$
$\Rightarrow x=\frac{{192}^{\circ }}{4}$
$\Rightarrow x={48}^{\circ }$

So, option b is correct.