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In figure, if line 1 is parallel to line 2, what is $x + y$ in terms of w and z?

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180 – w + z

180 + w – z

180 – w – z

180 + w + z

answer is A.

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Detailed Solution

Given a figure in which line 1 is parallel to line 2.
SOLVED] In the figure if l1||l2 what x + y in terms of w and z - Self Study 365

Use alternate angle property,
Since, y and z are interior opposite angles or alternate angles, therefore,

y = z

........……(i)
Also, x and w are consecutive interior angles.
Theorem states that if a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.
Therefore,

x + w = 180 ∘

..................(ii)
Add equations (i) and (ii).

⇒ x + y + w = 180 ∘ + z

⇒ x + y = 180 ∘ + z − w

Therefore, value of x + y is 180 – w + z.
Hence, option 1 is correct.

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