Find the measure of angle 𝐶.
Here’s angle 𝐶. How should we find the measure of this angle? Well, fortunately for us, we’re given two different measures, measure of angle 𝐴 and the measure of angle 𝐵 that can help us. These two angles are vertical angles because they’re opposite angles intersected by two lines. We know that vertical angles have the same angle measures.
We can also find the measure of angle 𝐶𝐵𝐴. Angle 𝐶𝐵𝐴 and angle 𝐴𝐵𝐹 are supplementary; they add up to one hundred and eighty degrees. They make a straight line, which means if we subtract one hundred and thirty four from one hundred and eighty, we can find the measure of angle 𝐶𝐵𝐴. Angle 𝐶𝐵𝐴 is forty six degrees.
We also know another key piece of information. The angles that make up a triangle always add up to one hundred and eighty degrees. We know two of the three angle measures of this triangle. Angle 𝐶 is that third measure. Fifty eight degrees plus forty six degrees plus the measure of angle 𝐶 equals one hundred and eighty degrees. We can add fifty eight plus forty six. Then we subtract one hundred and four degrees from both sides of our equation. One hundred and eighty degrees minus one hundred and four degrees equals seventy six degrees.
The measure of angle 𝐶 equals seventy six degrees.