Question

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

Answer 1

Answer:

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:

$\angle D +\angle E =180$

Substitute them for the equations:

$7x+21+15+5x=180$

Combine like terms and add on the left:

$12x+36=180$

Subtract 36 from both sides:

$12x=144$

Divide both sides by 12:

$x=12$

Thus, the value of x is 12.

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

So:

$\angle D+\angle C =180$

Substitute the equation for D:

$7x+21+\angle C=180$

Plug in 12 for x:

$7(12)+21+\angle C =180$

Simplify:

$84+21+\angle C =180\\105+\angle C =180$

Subtract 105 from both sides:

$\angle C =75\textdegree$

Thus, Angle C is 75 degrees.