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 $\angle a,\angle b,\angle c,\angle d.$

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
∠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^∘