Question

11. If PQ LIST Z PQR=110° and ZRST=130° find ZQRS.
S
2130
Or
If a transversal intersect two lines such that the bisectors of a pair of
corresponding angles are parallel, then prove that the two lines are
parallel​

Answer 1

Answer:

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= 1/2 ∠ABQ

In the same way,

∠BCF= 1/2 ∠BCS

Since BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,

∠ABE=∠BCF

1/2 ∠ABQ= 1/2 ∠BCS

∠ABQ=∠BCS

Therefore, by the converse of corresponding angle axiom,

PQ∥RS.

Answer 2

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