Question

Line ab is parallel to CD and line PQ is transversal measure of one angle is given find the measure of the following angles

Answer 1

(i) 75°.

(ii) 75°.

(iii) 105°.

(iv) 75°.

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Answer 2

Given that AB||CD and PQ is the transversal.

Now,

Angle BRT = 105 degrees

Now,

Angle ART = 180 - Angle BRT

(since, they are linear pair)

Thus,

Angle ART = 180-105 = 75 degrees

Angle CTQ = Angle ART

(since, they are corresponding Angles)

Thus,

Angle CTQ = 75 degrees

Also,

Angle DTQ = Angle BRT

(since, They are corresponding Angles)

Thus,

Angle DTQ =105 degrees

Again,

Angle PRB = Angle ART

(since, They are vertically Opposite Angles)

Thus,

Angle PRB = 75 degrees