In Fig., if l || m, n || p and ∠1 = 85°, find ∠2.

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Solution

In the given figure, l || m, n || p and ∠1 = 85°.
Now, let ∠4 be the adjacent angle of ∠2.
Thus, we have:
$∠ 3 = ∠ 1 = 85 ° (Corresponding angles)$
$∠ 3 + ∠ 2 = 180 °$ (Sum of interior angles on the same side of the transversal)
$∴ ∠ 2 = 180 ° - ∠ 3 = 180 ° - 85 ° = 95 °$

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