Parallel and transversal lines
Angles
We know that the angles
m∠XWZ = m∠XMN
m∠XYZ = m∠MNZ
The following pair of angles form a straight line (called supplementary angles):
m∠MNZ and m∠MNY
since the addition of supplementary angles is 180°, then
m∠MNZ + m∠MNY = 180°
Having this information we are going to complete the right cuadrilateral's angles:
Assuming that this is an isosceles trapezoid:
we have that the angles
m∠XMN and m∠MNY are equal, then
2x - 7 = 63
We want to find x from the equation:
2x - 7 = 63
↓ adding 7 both sides
2x = 63 + 7
2x = 70
↓ dividing both sides by 2
2x/2 = 70/2
x = 35°
Answer: x = 35°
Sides
We know that the lenght of the middle line is given by
[tex]\frac{\text{big segment + small segment}}{2}=Segment\text{ of the middle}[/tex]
Then
[tex]\frac{WZ+XY}{2}=MN[/tex]
replacing them with the given information:
[tex]\frac{(6x+11)+(4x-1)}{2}=60[/tex]
Now, we can find x
[tex]\begin{gathered} \frac{6x+11+4x-1}{2}=60 \\ \frac{10x+10}{2}=60 \\ 10x+10=60\cdot2 \\ 10x+10=120 \\ 10x=120-10 \\ 10x=110 \\ x=\frac{110}{11} \\ x=10 \end{gathered}[/tex]
Answer: x = 10
