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CBSE

Mathematics

Grade 8

Angles made by a Transversal

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Related Questions

In the figure, line l

is parallel to the line m

, and line p

is the transversal. Find the measure of x

.

Answer

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Hint: Here, we need to find the measure of the angle x

. We will use the property of alternate interior angles and linear pair angles to find the measure of the angle x

. The alternate interior angles on the opposite sides of a transversal, intersecting two parallel lines, are equal.

Complete step-by-step answer:

First, we will mark another angle in the given figure.

We will use the property of alternate interior angles and linear pair angles to find the measure of the angle x

.

It is given that line l

is parallel to the line m

, and line p

is the transversal.

Therefore, we get the alternate interior angles

∠1=60∘

Now, we will use the property of angles lying on a line, that is forming a linear pair.

From the figure, we can observe that the required angle x

and angle 1 form a linear pair.

Therefore, we get

⇒x+∠1=180∘

Substituting ∠1=60∘

in the equation, we get

⇒x+60∘=180∘

Subtracting 60∘

from both sides of the equation, we get

⇒x+60∘−60∘=180∘−60∘

Thus, we get

∴x=120∘