Question

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

Answer 1

75°

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.