The quadrilateral ABCD is a parallelogram if pairs of consecutive angles are supplementary. Given the angle measures, prove that quadrilateral ABCD is a parallelogram by finding the value of x. ∠A = 120 − 2x
∠B = 70 + x
∠ C = 1 0 5 − 2x
∠D = 40 + 4x

A) x = 2
B) x = 5
C) x = 10
D) x = 20

2) The quadrilateral ABCD is a parallelogram if both pairs of opposite sides are congruent. Given the side lengths, prove that quadrilateral ABCD is a parallelogram by finding the value of x.

AB = 2x + 55
A D = 4 0 + 2x
BC = 3x − 10
CD = 3x + 35

A) x = 2
B) x = 5
C) x = 10
D) x = 20

Astock has a 25% probability of increasing by $10 and a 75% probability of decreasing by $5. what is the stocks expected increase or decrease?

|y + 2| > 6 {y|y < -8 or y > 4} {y|y < -6 or y > 6} {y|y < -4 or y > 4}

Runners run around the school's football field. the cross country coach determines that the width of the field is seventy yards shorter than the length. part a write an expression that represents the perimeter of the football field. let x represent the length of the football field. include parentheses in your expression. next, write an equivalent expression that does not include parentheses. what property or properties did you use to simplify? explain. part b the cross country coach later determines that the length of the football field is 120 yards. all students must run five laps. using your answer from part a, determine the actual number of yards that each athlete must run in the tryouts. in order to make the team, students must complete the laps in 6 minutes. how quickly must they run each lap?