Question

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

Answer 1

Hint: In this problem, we are given that the supplement of an angle is one-third of itself, we have to determine the angle and its supplement. We can first assume a variable to find the angle we can then find the supplement of the assumed angle. We can then substitute the given condition for the assumed values to find the angle and its supplement.

Complete step by step answer:
Here we are given that the supplement of an angle is one-third of itself, we have to determine the angle and its supplement.
We can now assume \[{{x}^{\circ }}\] as the angle.
We know then the measure of its supplement angle will be \[{{\left( 180-x \right)}^{\circ }}\].
We are given that the supplement of angle is one-third of itself, we can write it as,
\[\Rightarrow 180-x=\dfrac{1}{3}x\]
We can now simplify the above steps, we get
\[\begin{align}
  & \Rightarrow 3\left( 180-x \right)=x \\
 & \Rightarrow 4x=540 \\
\end{align}\]
We can now divide 4 on both sides, we get
\[\Rightarrow x=\dfrac{540}{4}={{135}^{\circ }}\]
We can now substitute this value in the supplement angle, we get
\[\Rightarrow {{\left( 180-135 \right)}^{\circ }}={{45}^{\circ }}\]
Therefore, the required angle is \[{{135}^{\circ }}\] and the supplement angle is \[{{45}^{\circ }}\].

Note: We should always remember that the supplement angle are such angles whose measure adds up to \[{{180}^{\circ }}\], so we can subtract the angle from \[{{180}^{\circ }}\], to get the supplement of the given angle. We should know to solve the given condition by understanding what is given there.