Question

In the given figure, if l || m, then the value of x is Captionless Image (a) 30° (b) 45° (c) 60° (d) 75°​

Answer 1

Answer:

b ) 45 ° is the right answer

l||m

AB is the transversal

so angle B = angle A

angle a = 75°

angle b = 75-30 = 45

In a triangle sum of angles = 180

Consider ∆ ABC,

B = 45 (Above we find)

C = 90° ( given )

so x = 180-(45+90) =

180-135

= 45°

hope it helps you

pls follow if u like the answer

Answer 2

Given:

Line l is parallel to line m

To find:

The measure of angle x

Solution:

The measure of angle x is 45°.

We can find the angle by following the given steps-

We know that the ∆ACB is a right-angled triangle where angle C=90°.

Since l and m are parallel to each other, the alternate interior angles are equal.

So, angle ABm=75° (Alternate interior angles)

The angle CBm= 30° (Given)

This means that angle ABC+ angle CBm=angle ABm

On putting the values, we get

Angle ABC+30°=75°

Angle ABC=45°

Now, in ∆ACB, the sum of all angles is 180°.

Angle ABC+Angle ACB+Angle BAC=180°

Angle BAC= x°

We will add the values of angles,

45°+90°+x=180°

135°+x=180°

x=180°-135°

x=45°

Angle BAC, x=45°.

Therefore, the measure of angle x is 45°.