Question

14. Given parallelogram ABCD, find the lengths and angles required. (12 pts)

Answer 1

Answer:

a. x = 3

AB = 17

CD = 17

b. y = 18

m<A = 86°

m<D = 94°

Step-by-step explanation:

Based on the properties of a parallelogram, the following can be deduced:

AB = CD

m<A + m<D = 180°

m<A = m<C

m<B = m<D

a. ✔️Find the value of x

AB = CD

Substitute

5x + 2 = 8x - 7

Collect like terms

5x - 8x = -2 - 7

-3x = -9

Divide both sides by -3

x = 3

✔️Find AB and CD

AB = 5x + 2

Plug in the value of x

AB = 5(3) + 2 = 17

CD = 8x - 7

CD = 8(3) - 7 = 17

b. ✔️Find the value of y:

m<A + m<D = 180°

Substitute

2y + 50 + 3y + 40 = 180°

Add like terms

5y + 90 = 180

Subtract 90 from each side

5y = 180 - 90

5y = 90

Divide both sides by 5

y = 90/5

y = 18

✔️Find m<A and m<D

m<A = 2y + 50

Plug in the value of y

m<A = 2(18) + 50 = 86°

m<D = 3y + 40

m<D = 3(18) + 40 = 94°