In figure 2.9, 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

Given AB ||line CD and line PQ sis transversal .and∠ PRB 105°and ∠ BRT 105°

To find: ∠ ART, ∠ CTQ, ∠ DTQ, ∠ PRB

∠ ART + ∠ BRT = 180° ° (linear pair angle) means that linear pair is a pair of adjacent, supplementary angle.

Adjacent means next to each other, and supplementary means that measures of the two angles add up to equal 180 °.)

∠ ART + 105° = 180 (∠ BRT = 105 ° given)

∠ ART = 180° -105°

∠ ART = 75°

∠ ART ≅ ∠ PRQ (vertically opposite angles formed are congruent).

So, ∠ PRB = 75° (∵ ∠ ART 75°)

Line AB || line CD line PQ is transversal (given)

∠ BRT ≅ ∠ DTQ (corresponding angle theorem) if two parallel line are cut by a transversal, then the pairs of corresponding angle are congruent).

∠ DTQ = 105 (∠ BRT is 105°)

So that, ∠ DTQ = 105°

∠ ART ≅ ∠ CTQ (corresponding angle theorem) if two parallel line are cut by a transversal, then the pairs of corresponding angle are congruent).

So that, ∠ CTQ = 75° (because ∠ ART is 75°)