A transversal intersects a pair of parallel lines ab and cd at p and q

1.	A transversal intersects a pair of parallel lines ab and cd at p and q respectively. if the bisectors pm and qm of the angles apq and cqp meet at m what is angle pmqPLEASE GIVE EXPLANATION IN DETAIL
Answer» Step-by-step explanation: The transversal AD intersects the two lines PQ and RS at POINTS B and C respectively. BE is the bisector of ∠ABQ and CF is the bisector of ∠BCS. As, BE is the bisector of ∠ABQ, then, ∠ABE= 2 1 ∠ABQ In the same way, ∠BCF= 2 1 ∠BCS Since BE and CF are parallel and AD is the transversal, THEREFORE, by corresponding angle AXIOM, ∠ABE=∠BCF 2 1 ∠ABQ= 2 1 ∠BCS ∠ABQ=∠BCS Therefore, by the CONVERSE of corresponding angle axiom, PQ∥RS.

A transversal intersects a pair of parallel lines ab and cd at p and q respectively. if the bisectors pm and qm of the angles apq and cqp meet at m what is angle pmqPLEASE GIVE EXPLANATION IN DETAIL

Answer»

Step-by-step explanation:

The transversal AD intersects the two lines PQ and RS at POINTS B and C respectively. BE is the bisector of ∠ABQ and CF is the bisector of ∠BCS.

As, BE is the bisector of ∠ABQ, then,

∠ABE=

∠ABQ

In the same way,

∠BCF=

∠BCS

Since BE and CF are parallel and AD is the transversal, THEREFORE, by corresponding angle AXIOM,

∠ABE=∠BCF

∠ABQ=

∠BCS

∠ABQ=∠BCS

Therefore, by the CONVERSE of corresponding angle axiom,

PQ∥RS.