Question

A linear pair of angles is in the ratio 9:11 . The measure of the smaller angle is ?

Answer 1

Answer:

81 DEGREES

Step-by-step explanation:

LET THE PROPORTIONALITY CONSTANT BE X

THE ANGLES BE 9x AND 11x

9x+11x=180. (LINEAR PAIR)

20x=180

x=9

THE SMALLER ANGLE IS 9(9)

81 DEGREES

Answer 2

• The measure of the smaller angle = 81°.

Given :–

• A linear pair of angles in the ratio = 9 : 11.

To Find :–

• The measure of the smaller angle.

Solution :–

Let,

The first angle be 9x.

The second angle be 11x.

First, we need to find the value of x.

According to the question,

It is a linear pair.

We know that,

Sum of angles of the linear pair is 180°.

I.e.,

First angle + Second angle = 180°

Now,

$\implies 9x + 11x = 180 \degree$

$\implies 20x = 180 \degree$

$\implies x = \dfrac{18 \cancel0\degree}{2 \cancel0}$

$\implies x = \cancel\dfrac{18 \degree}{2}$

$\implies x = 9 \degree$

So, the angles are :

The first angle = 9x = 9 × 9° = 81°.

The second angle = 11x = 11 × 9° = 99°.

We have to find the smaller angle.

So, the first angle is the smaller angle.

I.e.,

First angle = Smaller angle

So, the smaller angle = 81°

Hence,

The measure of the smaller angle is 81°.