Question

name: quiz: parallel lines cut by transversal date: directions: fill in all angles and solve for the given variable when needed. 4) 5x 2x + 78 5) x + 28 2x 6) 3x + 50 5x

Explanation:

Step1: Use corresponding - angles property

When two parallel lines are cut by a transversal, corresponding angles are equal.
For problem 4:
We set up the equation \(5x=2x + 78\) since the two angles are corresponding angles.

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation \(5x=2x + 78\).
\(5x-2x=2x + 78-2x\), which simplifies to \(3x=78\).
Then divide both sides by 3: \(x=\frac{78}{3}=26\).

For problem 5:
We set up the equation \(x + 28=2x\) since the two angles are corresponding angles.

Step3: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation \(x + 28=2x\).
\(x+28 - x=2x - x\), which gives \(x = 28\).

For problem 6:
We set up the equation \(3x+50 = 5x\) since the two angles are corresponding angles.

Step4: Solve the equation for \(x\)

Subtract \(3x\) from both sides of the equation \(3x+50 = 5x\).
\(3x+50-3x=5x - 3x\), which simplifies to \(50 = 2x\).
Then divide both sides by 2: \(x=\frac{50}{2}=25\).

Answer:

For problem 4: \(x = 26\)
For problem 5: \(x = 28\)
For problem 6: \(x = 25\)