Answer:
[tex]x=8[/tex]
Step-by-step explanation:
Given
[tex]AB||CD[/tex]
[tex]\angle ABC = 5x + 50[/tex]
[tex]\angle BCD = 7x + 34[/tex]
Required
Find x
If [tex]AB||CD[/tex] i.e. If AB is parallel to CD, then
[tex]\angle ABC = \angle BCD[/tex]
Substitute values for ABC and BCD
[tex]5x + 50 = 7x + 34[/tex]
Collect Like Terms
[tex]5x - 7x = -50 + 34[/tex]
[tex]-2x = -16[/tex]
Multiply through by [tex]-\frac{1}{2}[/tex]
[tex]-\frac{1}{2} * -2x = -16 * -\frac{1}{2}[/tex]
[tex]\frac{1}{2} * 2x = 16 * \frac{1}{2}[/tex]
[tex]\frac{2x}{2} = \frac{16}{2}[/tex]
[tex]x = \frac{16}{2}[/tex]
[tex]x=8[/tex]
