In example 1, we can name this angle A or . There is only one angle. Its measurement can be determined by using a protractor. But clearly the measure is less than 90º since this is not as wide an angle as a right angle or square corner.
In example 2, there are several angles formed and they must be named carefully to avoid confusion. We can name by the three letters B, P, and C making sure that the vertex P is the middle letter: We see that . Similarly . Together, angles 1 and 2 form which is clearly larger than a square corner; therefore its measure will be larger than 90º.
If an angle A has measure , then is said to be acute. If an angle A has measure exactly , then is said to be a right angle. If an angle A has measure , then is said to be an obtuse angle.
The third angle B is also acute and is found by subtracting from as follows:
We calculate the measure of as follows: Therefore is acute.
Therefore is acute.
Therefore We subtract 80 and get Note that we say “an angle CPD has a measure of 48” while we say . Whether or not we use the degree symbol depends on the context and usually upon whether the word “measure” is used. This varies depending on different textbooks as well.