Question

1. if ( mangle1 = 3x - 3 ) and ( mangle5 = 7x + 23 ), for what value of ( x ) is ( ellparallel m )?
2. reason the transversal that intersects two parallel lines forms corresponding angles with measures ( mangle1 = 3x - 7 ) and ( mangle2 = 2x + 12 ). what is the measure of each angle?

Explanation:

Step1: Use the property of corresponding angles

When two parallel lines are cut by a transversal, corresponding angles are equal. So, \(m\angle1 = m\angle2\).
$$3x - 7=2x + 12$$

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
$$3x-2x - 7=2x-2x + 12$$
$$x - 7=12$$
Add \(7\) to both sides:
$$x-7 + 7=12 + 7$$
$$x = 19$$

Step3: Find \(m\angle1\)

Substitute \(x = 19\) into \(m\angle1=3x - 7\):
$$m\angle1=3\times19 - 7$$
$$m\angle1=57 - 7$$
$$m\angle1 = 50$$

Step4: Find \(m\angle2\)

Since \(m\angle1 = m\angle2\) (corresponding angles), \(m\angle2 = 50\)

Answer:

The measure of each angle (\(m\angle1\) and \(m\angle2\)) is \(50\)