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. 

1. ∠ART
2. ∠CTQ
3. ∠DTQ
4. ∠PRB

Answer 1

∠BRT = 105°   ...(Given)

(i) ∠ART + ∠BRT = 180°   ...(Angles in a linear pair)

∴ ∠ART + 105° = 180°

∴ ∠ART = 180° - 105°

∴ ∠ART = 75°

(ii) Line AB || line CD and line PQ is their transversal.

∴ ∠CTQ ≅ ∠ART   ...(Corresponding angles)

∴ ∠CTQ = ∠ART

∴ ∠CTQ = 75°

(iii) Line AB || line CD and line PQ is their transversal.

∴ ∠BRT = ∠DTQ    ...(Corresponding angles)

∴ 105^∘ = ∠DTQ     ...[From (i)]

∴ ∠DTQ = 105^∘

(iv) ∴ ∠PRB = ∠ART   ...(Vertically opposite angles)

∴ ∠PRB = 75^∘      ...(∠ART = 75^∘)