Question

The angle which is one fifth of its supplement is
A) \[15^\circ \]
B) \[30^\circ \]
C) \[45^\circ \]
D) \[60^\circ \]

Answer 1

Hint:
We have to find the angle using the given condition. We will use the concept of supplementary angles to find the angle. Two angles are said to be supplementary angles when they add up to 180 degrees. We will first find the supplement of an angle then divide it by 5 to get the required answer.

Complete step by step solution:
Two angles are said to be supplementary which add up to 180 degrees.
Supplementary angles are given by \[\angle A + \angle B = 180^\circ \].
Let the angle of the supplement be\[x\] and the angle which is one fifth of its supplement be \[\dfrac{1}{5}x\].
So, we get
\[ \Rightarrow x + \dfrac{1}{5}x = 180^\circ \]
By taking LCM on left hand side of the above equation, we get
\[ \Rightarrow x \times \dfrac{5}{5} + \dfrac{1}{5}x = 180^\circ \]
\[ \Rightarrow \dfrac{{5x}}{5} + \dfrac{x}{5} = 180^\circ \]
Now, adding the like terms, we get
\[ \Rightarrow \dfrac{{5x + x}}{5} = 180^\circ \]
\[ \Rightarrow \dfrac{{6x}}{5} = 180^\circ \]
Rewriting the equation, we get
\[ \Rightarrow 6x = 180^\circ \times 5\]
By cross multiplying, we get
\[ \Rightarrow 6x = 900^\circ \]
Dividing \[900^\circ \]by 6, we get
\[ \Rightarrow x = \dfrac{{900^\circ }}{6}\]
\[ \Rightarrow x = 150^\circ \]
Thus, one of the angles of supplement is \[150^\circ \]and the other angle is one fifth of \[150^\circ \]. Therefore,
\[\dfrac{{150^\circ }}{5} = 30^\circ \]
The angle which is one-fifth of its supplement is \[30^\circ \].
Therefore, the angle which is one-fifth of its supplement is \[30^\circ \].

Hence, option B is the correct answer.

Note:
The supplementary angles may be classified as either adjacent or nonadjacent. The adjacent supplementary angles share the common line segment or arm with each other, whereas the non-adjacent supplementary angles do not share the line segment or arm. The two angles together make a straight line, but the angles need not be together. “S'' of supplementary angles stands for the “Straight” line. This means they form \[180^\circ \].