Two parallel lines are cut by a transversal. Angles M and P are alternate interior angles. Angle M measures (10x + 50)° and angle P measures (12x + 30)°. What is the measure of angle M?

Your parallel line theorem says that alternate angles are equal, so solve

12x + 30 = 10x + 50

10

(2x+50) (8x+8) solve angle degree

To find the measure of angle M, we need to first set up an equation using the given information.

We are told that angles M and P are alternate interior angles. Alternate interior angles are congruent when a transversal intersects two parallel lines. So, we can set up the equation:

Angle M = Angle P

Now, substitute the given expressions for angles M and P into the equation:

10x + 50 = 12x + 30

Simplify the equation by combining like terms:

-2x = -20

To isolate x, divide both sides of the equation by -2:

x = 10

Now that we have found the value of x, we can substitute it back into the equation to find the measure of angle M:

Angle M = 10x + 50
= 10(10) + 50
= 100 + 50
= 150

Therefore, the measure of angle M is 150°.