Question

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 $x^{\circ }$.

Then its supplementary angle = $5x^{\circ }-{24}^{\circ }$

Then $x+5x-{24}^{\circ }={180}^{\circ }$ [Since the angles are supplementary]

$\Rightarrow 6x=({180}^{\circ }+{24}^{\circ })$

$\Rightarrow x=\frac{{204}^{\circ }}{6}$

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

$\therefore$ Measure of supplement angle is $5x^{\circ }-{24}^{\circ }=5\left({34}^{\circ }\right)-{24}^{\circ }={170}^{\circ }-{24}^{\circ }={146}^{\circ }$