Question

In the adjoining figure m and n are a pair of coplanar lines and l is the transversal intersecting them. If angle a= 60 degrees and angle g = 85 degrees then is m parallel to n?State reasons​

Answer 1

Answer:

Let us mark the points R and S on line p, T and U on line q, A and B on line l and C and D on line m.

Suppose the lines p and q intersect the line l at K and L respectively and line m at N and M respectively.

Since, AB is a straight line and ray KN stands on it, then

∠NKL + ∠NKA = 180∘ (Angles in a linear pair)

⇒110∘ + a = 180∘

⇒a = 180∘ − 110∘ = 70∘

Since, line p || line q and line l is a transversal intersecting them at K and L, then

∠TLB = ∠NKA (Alternate exterior angles)

⇒b = a

⇒b = 70∘

Since, line p || line q and line m is a transversal intersecting them at N and M, then

∠CNK = ∠NML (Corresponding angles)

⇒c = 115∘

Since, CD is a straight line and ray ML stands on it, then

∠NML + ∠LMD = 180∘ (Angles in a linear pair)

⇒115∘ + d = 180∘

⇒d = 180∘ − 115∘ = 65∘

Step-by-step explanation:

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