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9. In each of the following figures, L || M, find the values of x and y.
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Analysis
In this question, it is given that the lines l and m are parallel and line n is a transversal. We can derive the solution by using the various properties of two parallel lines cut by a transversal.
Solution,
∠ 100° = ∠ y [Alternate interior angles]
∠ x + ∠ y = 180° [∠ x and ∠ y form a straight line, hence they are supplementary]
∠ x + ∠ 100° = 180°
∠ x = 180 - 100
= 80°
Therefore,
∠ y = 100°
∠ x = 80°
Knowledge Bytes:
→ Properties of two parallel lines cut by a transversal
✳ Corresponding angles are equal.
✳ Alternate interior angles are equal.
✳ Alternate exterior angles are equal.
✳ Co-interior angles are supplementary.
✳ Vertically opposite angles are equal.
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