Can someone PLEASE show me how to work this out step by step????

Question

Given: ∠6≅∠7

Prove: ∠5≅∠8

Answer 1

∠5 and ∠6 are vertical angles (def of vertical angles)

∠5≅∠6 (vertical angles are congruent).

Repeat above steps for ∠7and ∠8

Now:

∠6≅∠7 (given)

At this point various ways to get to final statement, depending.....

But note that we have:

∠5≅∠6≅∠7≅∠8

So by transitive property for congruence the following can be deduced:

∠5≅∠8 (that which was to be proved, Q.E.D.)