Triangle $ABC$ is isosceles with angle $B$ congruent to angle $C$. The measure of angle $C$ is four times the measure of angle $A$. What is the number of degrees in the measure of angle $B$?
I know that the sum of the angles in a triangle is 180 degrees, so I can write an equation using that fact and the given information. Let x be the measure of angle $A$, then the measure of angle $C$ is 4x, and the measure of angle $B$ is also 4x, since they are congruent. The equation is $x + 4x + 4x = 180$. Simplifying, I get $9x = 180$, so $x = 20$. Therefore, the measure of angle $B$ is 4x, which is 4 times 20, or 80 degrees. 