Answer

Verified

359.7k+ 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 $y$.

**Complete step by step answer:**

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.

Recently Updated Pages

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Find the values of other five trigonometric ratios class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Describe the poetic devices used in the poem Aunt Jennifers class 12 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

And such too is the grandeur of the dooms We have imagined class 12 english CBSE

Where is the endless fountain of immortal drink pouring class 10 english CBSE

What I want should not be confused with total inactivity class 12 english CBSE

Why was the Moral Rearmament Army welcomed at the class 12 english CBSE

Difference Between Plant Cell and Animal Cell