Prove angle 1 and angle 5 are supplementary.
Prove angle 8 and angle 4 are congruent

The answer is below

Step-by-step explanation:

a)

∠1 ≅ ∠4               When two parallel lines are cut by a Transversal, the pair    

                            of angles on the outer side of each of those two lines

                             but on opposite sides of the transversal are Alternate    

                             Exterior Angles which are equal.

∠1 = ∠4                   Definition of Alternate exterior angles.

∠4 and ∠5 form      Definition of linear pair.

linear pair

∠4 and ∠5 are         If linear pair, then it is supplementary.

supplementary.

m∠4 + m∠5 = 180     Definition of supplementary

m∠1 + m∠5 = 180      Substitution property of equality

∠1 and ∠5 are           Definition of supplementary.

supplementary.

b)

∠5 ≅ ∠2               When two parallel lines are cut by a Transversal, the

                             angles in matching corners are called corresponding

                             angles which are equal. These angles are congruent.

∠2 ≅ ∠4                When two parallel lines are cut by a Transversal, the

                             angles in opposite positions relative to a transversal

                             are alternate angles. These angles are congruent.

∠5 ≅ ∠4                 Substitution property of equality

∠5 ≅ ∠8                When two parallel lines are cut by a Transversal, the

                             angles in opposite positions relative to a transversal

                             are alternate angles. These angles are congruent.

∠5 ≅ ∠4                 Substitution property of equality

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.