Video Transcript
Find the measure of angle ๐ถ.
Hereโs angle ๐ถ. How should we find the measure of this angle? Well, fortunately for us, weโre given two different measures, measure of angle ๐ด and the measure of angle ๐ต that can help us. These two angles are vertical angles because theyโre opposite angles intersected by two lines. We know that vertical angles have the same angle measures.
We can also find the measure of angle ๐ถ๐ต๐ด. Angle ๐ถ๐ต๐ด and angle ๐ด๐ต๐น 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 ๐ถ๐ต๐ด. Angle ๐ถ๐ต๐ด 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 ๐ถ is that third measure. Fifty eight degrees plus forty six degrees plus the measure of angle ๐ถ 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 ๐ถ equals seventy six degrees.