In triangle ABC, the measure of <A is 86 degrees. The measure of <B is 22 degrees more than three times the measure of <C. What is the measure, in degrees, of <C?
B = 3C + 22
86 + B + C = 180
Substitute 3C+22 for B in the second equation and solve for C.
To find the measure of angle C, we need to set up an equation using the given information.
We know that the measure of angle A is 86 degrees.
Let's assume that the measure of angle C is x degrees.
According to the second piece of information, the measure of angle B is 22 degrees more than three times the measure of angle C. Therefore, the measure of angle B can be represented as 3x + 22 degrees.
In any triangle, the sum of the measures of the three interior angles is always 180 degrees. So, we can write the equation:
A + B + C = 180
Substituting the given values into the equation, we have:
86 + (3x + 22) + x = 180
Simplifying the equation, we get:
86 + 3x + 22 + x = 180
4x + 108 = 180
4x = 180 - 108
4x = 72
Dividing both sides by 4, we find:
x = 72/4
x = 18
Therefore, the measure of angle C is 18 degrees.
To summarize:
In triangle ABC, the measure of angle C is 18 degrees.