Question

please help me with this
solve with explanation...​

Answer 1

Answer:

Proven that:

i. ∠1 = ∠2

ii.  ∠1 = ∠2 = ∠3 = ∠4

Step-by-step explanation:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

PS and QR are opposite sides of the parallelogram.  i.e. PS and QR are parallel lines and Line SR is a traversal.

Therefore, ∠1 = ∠4.

Now, lets extend line SP in the direction S to P and further.  We will get ∠5 corresponding to ∠4 since SR and PQ are parallel lines and line SP is a traversal.  By same argument ∠4 = ∠5.  Now ∠5 = ∠2 since they are vertical angles.  Therefore, ∠1 = ∠4 = ∠5 = ∠2.  That is ∠1 = ∠2.  This proves question (i).

Now ∠2 and ∠3 are corresponding angles, as PS and QR are parallel lines and line PQ is a traversal.  Therefore, ∠2 = ∠3.

Combining the above, ∠1 = ∠2 = ∠3 = ∠4