Question

Find the measure of an angle, if six times of its complement is ${12}^{\circ }$ less than twice of its supplement

• A. ${42}^{\circ }$
• B. ${96}^{\circ }$
• C. ${24}^{\circ }$
• D. ${58}^{\circ }$

Answer 1

The correct option is

A

${42}^{\circ }$

let angle be $x$

complement $90-x$

supplement $180-x$

$6(90-x)=2(180-x)-12$ $\left\{Given\right\}$

$540-6x=360-2x-12$

$180-12$ = $4x$
$4x=168$

$x={42}^{\circ }$