Question

Two adjoining angles are supplementary to each other if their sum is ${180}^{\circ }$. The supplement of an angle is 24 less than 5 times the angle.

Find the measure of the supplement.

• A. ${136}^{\circ }$
• B. ${126}^{\circ }$
• C. ${116}^{\circ }$
• D. ${146}^{\circ }$

Answer 1

The correct option is D

${146}^{\circ }$

Let the angle be $x^{\circ }$

The supplement of $x^{\circ }$ is $(180-x{)}^{\circ }$

$\Rightarrow (180-x)=5x-24$

$\Rightarrow 5x+x=180+24$

$\Rightarrow 6x=204$

$\Rightarrow x={34}^{\circ }$

$\therefore Thesupplement=(180-34)={146}^{\circ }$