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Question
In the given figure, if l1 || l2 and l3 || l4, what is y in terms of x?
Options
90 + x
90 + 2x
`90 + x/2`
90 − 2x
Solution
The given figure is:
Here, we have ∠2 and 2y are vertically opposite angles. Therefore,
∠2 = 2y ...(i)
∠1 and x are alternate interior opposite angles.
Thus,
∠1 = x ...(ii)
∠1 and ∠2 are consecutive interior angles.
Theorem states: If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.
Thus,
∠1 + ∠2 180°
From (i) and (ii), we get:
x +2y = 180°
2y = 180° - x
`y = (180° -x)/2`
`y = (180°)/2 - x /2`
`y = 90° - x /2`
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