Question

find solution
in the given figure AB and CD are intersected by a transversal PS Is AB ||CD? explain.

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Answer 1

Line AB is parallel to CD.

Step-by-step explanation:

• We can see that the transversal P cuts the line AB at point Q and line CD at point R.

Also, it is given that;

• $\angle PQA = 100^o$

So,  $\angle AQR = 180^o - \angle PQA$  [Because, $\angle PQA + \angle AQR = 180^o$]

Thus,  $\angle AQR = 180^o - 100^o = 80^o$

Also, it is given that;

• $\angle SRC = 80^o$

So,  $\angle CRQ = 180^o - \angle SRC$  [Because, $\angle SRC + \angle CRQ = 180^o$]

Thus,  $\angle CRQ = 180^o - 80^o = 100^o$

• Now, we can see that$\angle CRQ = \angle AQP = 100^o$

Here, we observe that lines AB & CD make the same angles as 100^o with line tansversal P. So, LIne AB is parallel to line CD.  

 So, Line AB is parallel to CD.