# 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. ∠ CTQiii. ∠ 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°)

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