Question

P R А" 105° B 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) ZART (ii) ZCTO (iii) ZDTQ (iv) ZPRB C T Т. Fig. 2.9

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Answer 1

Answer:

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°)