In the adjoining figure if AB ∥ CD then the value of x is–
2022
In the adjoining figure if AB ∥ CD then the value of x is–
- A.
60
- B.
80
- C.
90
- D.
100
Attempted by 39 students.
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Correct answer: D
To find the value of x in the given figure, where line AB is parallel to line CD, we can use the properties of alternate interior angles.
Step-by-Step Solution
Geometric Construction: Draw a straight line passing through point O that is parallel to both line AB and line CD. Let’s call this line L.
Apply Alternate Interior Angles:
Since AB is parallel to L, the angle AOB (given as 80°) and the upper part of angle x are alternate interior angles. Therefore, the upper part of x equals 80°.
Similarly, since CD is parallel to L, the angle OCD (given as 20°) and the lower part of angle x are alternate interior angles. Therefore, the lower part of x equals 20°.
Calculate x: Angle x is the sum of these two parts:
x = 80° + 20° = 100°