Question

Can someone please help me I don't understand and I'm trying to learn this :((​

Answer 1

∠G = 135

EF = 12

Explanation:

In parallelogram, adjacent angles are supplementary

∠G + ∠F = 180

7x - 5 + 3x - 15 = 180 {combine like terms}

10x - 20 = 180

10x = 180 + 20

10x = 200

x = 200/10

x = 20

∠G = 7x - 5 = 7*20 -5 = 140 - 5 = 135

In a parallelogram, opposite sides are equal.

EF = GH

3y = y +8

3y - y = 8

2y = 8

y = 8/2

y = 4

EF = 3y = 3*4 = 12

Answer 2

In a parallelogram the two angles on the same side need to equal 180 degrees. So in the picture angle F and angle G need to equal 180:

Add them together:

7x -5 + 3x-15 = 180

Simplify by combining like terms:

10x -20 = 180

Add 20 to both sides:

10x = 200

Divide both sides by 10:

X = 20

Now you know x, replace x in the angle for g and solve:

G= 7x-5 = 7(20) -5 = 140-5 = 135

G = 135 degrees.

In a parallelogram the top and bottom are the same length, so set the two to equal each other and solve for y:

3y = y + 8

Subtract y from both sides:

2y = 8

Divide both sides by 2:

Y = 4

Now replace y and solve for EF:

EF = 3y = 3(4) = 12

EF = 12