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Question
In the given figure, if l1 || l2, what is the value of y?
Options
100°
120°
135°
150°
Solution
Given figure is as follows:
It is given that l1 || l2.
∠1 and 3x are vertically opposite angles, which must be equal, that is,
∠1 = 3x (i)
Also, ∠1and x are consecutive interior angles.
Theorem states: If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.
Thus,
∠1 + x = 180°
From equation (i), we get:
`3x + x = 180°`
`4x = 180°`
` x = 180°/4`
`x = 45°`
x and y form a linear pair. Therefore, their sum must be supplementary.
Thus,
y + x =180°
Substituting, x = 45° in equation above, we get:
y + 45° = 180°
y = 180° - 45°
y = 135°
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