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:
[tex]\angle D +\angle E =180[/tex]
Substitute them for the equations:
[tex]7x+21+15+5x=180[/tex]
Combine like terms and add on the left:
[tex]12x+36=180[/tex]
Subtract 36 from both sides:
[tex]12x=144[/tex]
Divide both sides by 12:
[tex]x=12[/tex]
Thus, the value of x is 12.
Note that Angle D and Angle C are also adjacent. Thus, their angles also equal 180.
So:
[tex]\angle D+\angle C =180[/tex]
Substitute the equation for D:
[tex]7x+21+\angle C=180[/tex]
Plug in 12 for x:
[tex]7(12)+21+\angle C =180[/tex]
Simplify:
[tex]84+21+\angle C =180\\105+\angle C =180[/tex]
Subtract 105 from both sides:
[tex]\angle C =75\textdegree[/tex]
Thus, Angle C is 75 degrees.
