The value of x° in the given diagram is 150°. This is obtained by using the pair of interior angles formed along a transverse when passing through parallel lines.
What are the interior angles?
- The angles that lie inside or in-between region of the parallel lines when a transverse passes through them are said to be pair of Interior angles.
- These angles are on the same side of the transverse.
- The sum of these angles is 180°.
What are the verticle angles?
The verticle angles are opposite to each other when two lines are intersected at a point. Those angles are the same in size.
Calculating the angle x:
It is given that line AB is parallel to line CD and transverse is making angles with these lines.
The angles are x° and 30°.
The angle of 30° is at the exterior side of these lines at the point of intersection of line CD and the transverse line. So, it forms a verticle pair of angles with the angle opposite to it.
Thus, the angle opposite to it also becomes 30°. This opposite angle lies inside the parallel lines. So it forms a pair of interior angles with a given angle x.
Since we know that sum of pair of interior angles = 180°, we get
x° + 30° = 180°
⇒ x° = 180° - 30°
⇒ x° = 150°
∴ x = 150°
Thus, the angle x = 150°. So, option C is correct.
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