Question

↔ AB || CD in the following figure. ↔ XY is the transversal. If m∠PQA = 140°, find the measure of remaining angles:

Answer 1

SOLUTION:-
GIVEN BY:- AB || CD
》∠PQA = 140.
》IF AB || CD
》then,
》∠PQA = ∠BQY = 140
》∠PQB = 180-∠PQA.
》∠PQB = 180-140 = 40
》∠PQB = ∠AQY = 40
and,
》∠PQB = ∠XPD = 40
》∠XPD = ∠CPQ = 40
》∠PQA = ∠CPX = 140

》∠CPX = ∠QPD = 140


■I HOPE ITS HELP■

Answer 2

Given ,
AB || CD ,
and XY is the transversal , m∠PQA = 140° .

We know that four pairs of angles are formed .

Linear pairs , Angles on a straight line sum to 180

∠PQA + ∠ PQB = 180°
140 + ∠ PQB = 180
∠ PQB = 180 - 140 = 40°

Vertically opposite angles are equal ,
∠PQA = ∠BQY
140° = ∠BQY

Another pair of vertically opposite angles ,
∠BQP = ∠AQY
40 = ∠AQY

Also , Sum of angles interior to the parallel lines on the same side are supplementary .
Co-interior angles are supplementary .

∠DPQ + ∠PQB = 180°
∠DPQ + 40 = 180°
∠DPQ = 180 - 40
∠DPQ = 140°


Linear pair :
∠DPQ + ∠CPQ = 180
∠CPQ = 180 - 140 = 40°

Vertically opposite angles ,
∠CPQ = ∠XPD
40° = ∠XPD


∠DPQ = ∠XPC
140° = ∠XPC

Hope helped !