Question

Help me on finding the angles

Answer 1

Use the fact that the lines are parallel and there is a transversal

∠4 = 106° 
∠3 = 50° 
∠5 = 50° 
∠8 = 106°
∠7 = 106° 

Answer 2

You are given that that m∠1 = 106° and m∠2 = 50° and PQ║JK

Since PQ and JK are parallel, then because of the alternate interior angles theorem, ∠5 = ∠2, so ∠5 = 50° as well.

∠1 and ∠8 are corresponding angles so therefore they are equivalent and ∠8 = 106°.

∠4 and ∠8 are corresponding so they are equivalent as well and ∠4 = 106°.

∠3 is alternate interior angles with ∠5 which we already found, so they are equivalent and ∠3 = 50°

∠7 and ∠8 are vertical angles so ∠7 = ∠8. We already found ∠8, it is 106°. Therefore ∠7 = 106°.

In summary,
∠4 = 106° because of corresponding angles with ∠8
∠3 = 50° because of alternate interior angles with ∠5
∠5 = 50° because of alternate interior angles with ∠3
∠8 = 106° because of corresponding angles with ∠1
∠7 = 106° because of vertical angles with ∠8

Hope this helps! ^-^