In Fig 8.112, if l||m, n||p and ∠1 =85°, find ∠2.
Answers
Concept :
Corresponding angle :
Two angles on the same side of a transversal are known as the corresponding angles if both lie either above the two lines or below the two lines.
Given : l || m, n || p and ∠1 = 85°.
We know that, when a line cuts the parallel lines, the pair of corresponding angles are equal :
=> ∠1 = ∠3 = 85°
Again, co-interior angles are supplementary i.e 180°. so
∠2 + ∠3 = 180°
∠2 + 55° = 180°
∠2 = 180° – 85°
∠2 = 95°
Hence the value ∠2 is 95°.
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Similar questions :
In Fig 8.111, state which lines are parallel and why?
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If, l, m, n are three lines such that l||m and n⊥ l, prove that n⊥ m.
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Answer:
As per the diagram,
n∣∣p and m is transversal.
∠1=∠3 [ Corresponding angles are equal ]
∠1=∠3=85
∠3+∠2=180 ( sum of cointerior angles is 180 )
85 +∠2=180
∠2=180 -85
∴∠2=95 ^0