Question

Find z

Help me please

Answer 1

Answer: z=56

Explanation:

Based on the figure, we can determine that 3y+8=68 and 4x=2z. With the knowledge that a trapezoid has 360°, we can first find the value of y to get the angle measures of the top angles. We can then subtract that from 360°.

3y+8=68 [subtract both sides by 8]

3y=60 [divide both sides by 3]

y=20

We now know the value of y is 20, but that is not relevant to solving this problem because we already know that the top angles are 68° each. So, we can subtract that from 360.

360-68-68=224

Now, we know that the bottom 2 angles have to add up to 224. Therefore, we can come up with 2 equations.

Equation 1: 4x=2z

Equation 2: 4x+2z=224

We can manipulate Equation 1 to be
`x=(1)/(2)z`. Once we plug that into Equation 2, we can find the value of z.

`4((1)/(2) z)+2z=224` [multiply]

`2z+2z=224` [add]

`4z=224` [divide both sides by 4]

`z=56`

Now, we know that z=56.