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°
