One angle of a triangle measures 120 degrees. The other two angles are congruent. Write and solve an equation to find the measure of the congruent angles.
To solve this problem, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's call the measure of the congruent angles "x" degrees.
Since the other two angles are congruent, each of them measures x degrees.
So, the equation can be written as:
x + x + 120 = 180
To solve this equation, combine like terms:
2x + 120 = 180
Next, we'll isolate the variable x by subtracting 120 from both sides:
2x = 180 - 120
2x = 60
Finally, we'll solve for x by dividing both sides by 2:
x = 60 / 2
x = 30
Therefore, the measure of each of the congruent angles is 30 degrees.