In the figure, line is parallel to the line is parallel to the line , and line , and line is the transversal. The measure of is the transversal. The measure of is ____ degree.

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Detailed Solution

Concept- The measure of angle ‘x’ is 120 degrees. In this case, we need to calculate the angle x. To obtain the measure of the angle x, we will utilize the property of alternate interior angles and linear pair angles. The alternative inner angles of two parallel lines intersected by a transversal are equal.
We will use the property of alternate interior angles and linear pair angles to find the measure of the angle

.
It is given that line

is parallel to the line

, and line

is the transversal.
Therefore, we get the alternate interior angles

Finally, by using the property of angles which lie on line and that formed a linear pair.
From the figure, we can observe that the required angle

and angle 1 forms a linear pair.
Therefore, we get

Substituting

in the equation, we get

Subtracting

from both sides of the equation, we get

Thus, we get

Hence, the correct answer is 120 degrees.