M∠a = 100 + 5x m∠b = 77 − 4x m∠c = 106 + 3x m∠d = 47 + 6x quadrilateral abcd is a parallelogram if both pairs of opposite angles are congruent. prove that quadrilateral abcd is a parallelogram by finding the measures of the opposite angle pairs? a) 95°, 85° b) 105°, 75° c) 115°, 65° d) 125°, 55°

C)115°, 65°

Step-by-step explanation:

A and C are opposite angles

A = C

100 + 5x = 106 + 3x

Subtract 3x from each side

100 + 5x-3x = 106 +3x-3x

100 + 2x = 106

Subtract 100 from each side

100-100 + 2x = 106-100

2x = 6

Divide by 2

2x/2 =6/2

x=3

Angle A = 100+ 5x

               =100 + 5(3)

               = 100+15

               = 115

Angle C = 115

Angle B = 77 - 4x

              = 77 -4(3)

              = 77-12

              = 65

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.