Question

In the given figure, line AB || line CD and line PQ is transversal. Measure of one of the angles is given. Hence find the measures of the following angles.

(i) ∠ART

(ii) ∠CTQ

(iii) ∠DTQ
(iv) ∠PRB

Answer 1

(i) Since AB is a straight line and ray RT stands on it, then
∠ART + ∠BRT = 180^∘ (Angles in a linear pair)
⇒∠ART + 105^∘ = 180^∘
⇒∠ART = 180^∘ − 105^∘ = 75^∘

(ii) Since line AB || line CD and line PQ is a transversal intersecting them at R and T, then
∠ART = ∠CTQ (corresponding angles)
⇒75^∘ = ∠CTQ
⇒∠CTQ = 75^∘

(iii) Since line AB || line CD and line PQ is a transversal intersecting them at R and T, then
∠BRT = ∠DTQ (corresponding angles)
⇒105^∘ = ∠DTQ
⇒∠DTQ = 105^∘

(iv) Since line AB and line PQ intersect at point R, then
∠PRB = ∠ART (vertically opposite angles)
⇒∠PRB = 75^∘ (∵ ∠ART = 75^∘)