Question

line AB// line CD & line pq is transversal. angle BRT=115 ,find the measure of angle CTQ and RTD

Answer 1

Answer:

Step-by-step explanation:

∠BRT+ ∠RTD=180° (CO INTERIOR ANGLE)

∠RTD= 180°-115°=65°

∠RTD=CTQ =65°   (VERTICALY  OPPOSITE ANGLE)

Answer 2

Given- AB ||line CD

and line PQ is transversal .

∠ BRT 105°

To find: ∠ ART, ∠ CTQ, ∠ DTQ, ∠ PRB

Solution- ∠ ART + ∠ BRT = 180° (linear pair angle)

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

∠ ART = 180° -105°

∠ ART = 75°

∠ ART ≅ ∠ PRB (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)

∠ DTQ = 105 (∠ BRT is 105°)So that, ∠ DTQ = 105°

∠ ART ≅ ∠ CTQ (corresponding angle theorem)

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

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