Question

Draw a figure in which ↔AB || ↔CD. ↔XY is a transversal. ↔XY intersects ↔AB at point P and ↔CD at point Q. If ∠XPA = 120°, find the measure of ∠PQD and ∠BPQ.

Answer 1

Acc to the question,

angle APX is 120 degree.

Since angle BPY is vertically opposite to angle APX, its value is equal to 120 degree as well.

We know, angle APX + angle APY = 180 degree.

Therefore, angle APY = 180 degree - angle APX = 180 - 120 = 60 degree.

Since angle APY is vertically opposite to angle BPX, so both the values will be the same. i.e. angle BPX = 60 degree.

Also, angle BPX is corresponding to angle DQX, therefore, angle DQX = 60 degree.

Similarly, CQY = 60 degree [ vertically opposite ]

angle CQX + angle CQY = 180 degree

We get, angle CQX = 120 degree = angle DQY [ vertically opposite ]

Answer 2

Given AB//CD, XY is the transversal.

i ) <1 = <3 = 120°

[ vertically opposite angles ]

<BPQ = <3 = 120°

ii ) <3 + <6 = 180°

[ Sum of interior angles same side

of the transversal are supplementary ]

=> 120° + <6 = 180°

=> <6 = 180° - 120°

=> <6 = 60°

<PQD = <6 = 60°

Therefore ,

<BPQ = 120° ,

<PQD = 60°

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