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In the figure given below, if $l 1 | | l 2$ and $I 3 | | I 4,$ and what is the measure of $y$ what is the measure of in terms of $x$ in terms of ?

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90 ° + x

90 ° − x

90 ° + 2 x

90 ° − x 2

answer is D.

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Detailed Solution

It is given that the lines

l 1 | | l 2

and

I 3 | | I 4 .

From the figure,

∠ 2

and

2 y

are vertically opposite angles and hence, they are equal.

∴ ∠ 2 = 2 y

Using the alternate interior angles property, we have,

∠ 1 = x

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary. From the above two equations, we have,

∴ ∠ 1 + ∠ 2 = 180 °

From the above two equations, we have,

x + 2 y = 180 °

⇒ y = 90 ° − x 2

Therefore, if

l 1 | | l 2

and

I 3 | | I 4,

then the measure of

y

in term of

x

90 ° − x 2 .

Hence, option (4) is correct.

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