Triangle $ABC$ is isosceles with angle $A$ congruent to angle $B$. The measure of angle $C$ is 30 degrees more than the measure of angle $A$. What is the number of degrees in the measure of angle $C$?
I know that the sum of the angles of any triangle is 180 degrees. So, if I call angle $A$ by $x$, then angle $B$ is also $x$, and angle $C$ is $x + 30$. Then I can write an equation: $x + x + (x + 30) = 180$. Simplifying, I get $3x + 30 = 180$, or $3x = 150$. Dividing both sides by 3, I get $x = 50$. This means that angle $A$ and angle $B$ are both 50 degrees, and angle $C$ is $x + 30$, or $50 + 30$, which is 80 degrees. 