Question

In the given figure, line p || line q and line l and line m are transversals. Measures of some angles are shown.

Hence find the measures of, ∠a, ∠b, ∠c, ∠d.

Answer 1

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

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

⇒ 110^∘ + a = 180^∘ 

⇒ a = 180^∘ − 110^∘ 

⇒ a = 70^∘

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

(ii) ∠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

(iii) ∠CNK = ∠NML    ...(Corresponding angles)

⇒ c = 115^∘

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

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

⇒ 115^∘ + d = 180^∘ 

⇒ d = 180^∘ − 115^∘ 

⇒ d = 65^∘