Question

in the given figure, PQ || RS and A is any point between the two lines. Prove that angle ABQ+ angle ACS= angle BAC.​

Answer 1

Answer:

Construction

draw a line LM (from left to right) parallel to PQ and RS and which passes through A.

Now

LM || PQ

angle QBA = angle BAL (alternate interior angles)..(1)

again

LM || RS

angle ACS = angle CAL(alternate interior angles)..(2)

adding (1) and (2)

angle QBA + angle ACS = angle BAL + angle CAL

angle QBA + angle ACS = angle BAC

proved