Find the measure of angle C in the parallelogram. Round your answer to the nearest degree

75°

Step-by-step explanation:

In a parallelogram, any two adjacent angles are supplementary. In other words, they total 180.

Angle D and Angle E are adjacent. Thus, they are supplementary. In other words:

Substitute them for the equations:

Combine like terms and add on the left:

Subtract 36 from both sides:

Divide both sides by 12:

Thus, the value of x is 12.

Note that Angle D and Angle C are also adjacent. Thus, their angles also equal 180.

So:

Substitute the equation for D:

Plug in 12 for x:

Simplify:

Subtract 105 from both sides:

Thus, Angle C is 75 degrees.