Question

The supplement of an angle is one-fifth of itself. Determine the angle and its supplement.

• A. 50° and 130°
• B. 150° and 50°
• C. 30° and 120°
• D. 150° and 30°

Answer 1

The correct option is D

150° and 30°

Explanation for the correct option:

Option: (D)

Finding the value of $x$:

Given data: Supplement of an angle is $\frac{1}{5}$of itself.

As we know that if the sum of two angles equal to 180° then they are supplementary angles.

We need to find the value of two angles.

Let one angle = $x°$

Second angle = $(180-x)°$

According to the given data,

$$\begin{gathered} x=\frac{1}{5}\left(180°-x\right) \\ \Rightarrow 5x=180°-x \\ \Rightarrow 5x+x=180° \\ \Rightarrow 6x=180° \\ \Rightarrow x=30° \\ \therefore x=30° \end{gathered}$$

Now, substituting the value of $x$ in $\left(180°-x\right)$ in order to find the second angle.

Second angle = $\left(180-x\right)$

= $\left(180-30\right)$

= $150°$

Therefore, the two angles are $30°$ and $150°$

Hence, Option (D) is the correct answer.