Question

in the figure line AB || line CD and line PQ is transversal . measure of one of the angles is given . hence find the measure of the following angles.
1. angle ART
2.angle CTQ
3.angle DTQ
4.angle PRB​

Answer 1

Answer:

Given: AB Il CD and PQ is the transversal.

To find : (i) <ART

(ii) <CTQ

(iii) <DTQ

(iv) <PRB

Solution :

(i) <ART + <BRT = 180° (Linear Pair)

=> <ART + 105° = 180°

=> <ART = 180° -105°

=> <ART = 75°

(ii) <CTQ = <ART (corresponding Angles)

=> <CTQ = 75°

(iii) < DTQ + <CTQ = 180° (Linear Pair)

=> <DTQ + 75° = 180°

=> <DTQ = 180° - 75°

=> <DTQ = 105°

(iv) <PRB = <ART (Vertically Opposite Angles)

=> <PRB = 75°

Hope it helps you

Thanks