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In figure, if $I / / m, n / / p$ and $∠ 1 = 85 °,$ the measure of $∠ 2$ is:

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35 ∘

75 ∘

95 ∘

65 ∘

answer is C.

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Detailed Solution

Given a figure in which

I | | m, n | | p

and

∠ 1 = 85 °

As, m is the transversal on parallel lines n and p.
Corresponding angle property states that if a transversal intersects two parallel lines, the corresponding angles will be always equal.
Hence, using corresponding angles property,

∠ 3 = ∠ 1 = 85 °

Similarly, p is transversal on parallel lines m and l.
Hence, using interior angles the sum should be equal to

180 ∘

∠ 2 + ∠ 3 = 180 °

⇒ ∠ 2 = 180 ° − 85 ° [∵ ∠ 3 = 85 °]

⇒ ∠ 2 = 95 °

Therefore, measure of

∠ 2

95 ∘

.
Hence, option 3 is correct.

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