Question

The measure of an angle which is five times its supplement is

• A. ${36}^{\circ }$
• B. ${30}^{\circ }$
• C. ${150}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is C ${150}^{\circ }$

Given,

An angle is $5$ times its supplement

Let the angle be $a$ and its supplement be $b$

Then, $a=5b$........(1)

As, a and b are supplementary

$\therefore a+b={180}^{\circ }$

According to question,

$a+b=180$

$\Rightarrow a+b=5b+b=6b=180$

$\Rightarrow 6b=180$

$\Rightarrow b=30$

$\because a=5b$

$\therefore a=5\cdot {30}^{\circ }$

$\Rightarrow a={150}^{\circ }$

Hence, the answer is option $C$.