Question

find the value of the variable(s) in each figure.
7.
8.

Explanation:

Step1: For problem 7

When two parallel lines \(l\) and \(m\) are cut by a transversal \(k\), the alternate - interior angles are equal. So, we set up the equation \(6x + 4=8x - 8\).
Subtract \(6x\) from both sides:
\(6x+4-6x = 8x - 8-6x\)
\(4=2x - 8\)
Add \(8\) to both sides:
\(4 + 8=2x-8 + 8\)
\(12 = 2x\)
Divide both sides by \(2\):
\(x=\frac{12}{2}=6\)

Step2: For problem 8

When two parallel lines \(l\) and \(m\) are cut by a transversal \(k\), the corresponding angles are equal. So, we set up the equation \(4x-10 = 3x + 10\).
Subtract \(3x\) from both sides:
\(4x-10-3x=3x + 10-3x\)
\(x-10 = 10\)
Add \(10\) to both sides:
\(x-10 + 10=10 + 10\)
\(x = 20\)

Answer:

For problem 7: \(x = 6\)
For problem 8: \(x = 20\)