Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# The measure of an angle which is $9$ times its supplement.A. $162$B. $81$C. $90$D. $10$

Last updated date: 14th Aug 2024
Total views: 411k
Views today: 6.11k
Verified
411k+ views
Hint: We will assume the supplement angles as $x$ and $y$. We have the relation between supplement angles as $x+y=180{}^\circ$. In the problem they have mentioned the angle $x$ is $9$ times its supplement, then we will get a relation between $x$ and $y$. From these two relations we can find the values of both $x$ and $y$.

Let $x$ and $y$ be the supplement angles.
We know that the sum of the supplement angles is equal to $180{}^\circ$.
$\therefore x+y=180{}^\circ ...\left( \text{i} \right)$
In the problem, we have given that the one angle is $9$ times its supplement, then we will get
$x=9y$ or $y=9x$

If $x=9y$, from equation $\left( \text{i} \right)$ the value of $y$ is given by

\begin{align} & x+y=180{}^\circ \\ & \Rightarrow 9y+y=180{}^\circ \\ & \Rightarrow 10y=180{}^\circ \\ \end{align}
Dividing with $10$ on both sides of the above equation, then we will have
\begin{align} & \Rightarrow \dfrac{10y}{10}=\dfrac{180{}^\circ }{10} \\ & \Rightarrow y=18{}^\circ \\ \end{align}
Now the value of $x$ is $9y=9\times 18{}^\circ =162{}^\circ$.

So, the correct answer is “Option A”.

Note: In this problem they have mentioned that the angles are supplementary. So, we have taken the sum of the angles as $180{}^\circ$. If they have mentioned that the angles are complementary, then we need to take the sum of the angles as $90{}^\circ$ and follow the same procedure to find the angles.