Step-by-step explanation:
An angle is formed by two rays that share a common endpoint. Each ray is called a side of the angle and the common endpoint is called the vertex. An angle is named by its vertex. In the image below, ∠A is the angle with vertex at point A. The measure of ∠A is written m∠A.
∠A is the angle with vertex at point A.
The image is an angle made up of two rays. The angle is labeled with letter A.
We measure angles in degrees, and use the symbol ∘ to represent degrees. We use the abbreviation m to for the measure of an angle. So if ∠A is 27∘, we would write m∠A=27.
If the sum of the measures of two angles is 180∘, then they are called supplementary angles. In the images below, each pair of angles is supplementary because their measures add to 180∘. Each angle is the supplement of the other.
The sum of the measures of supplementary angles is 180∘.
Part a shows a 120 degree angle next to a 60 degree angle. Together, the angles form a straight line. Below the image, it reads 120 degrees plus 60 degrees equals 180 degrees. Part b shows a 45 degree angle attached to a 135 degree angle. Together, the angles form a straight line. Below the image, it reads 45 degrees plus 135 degrees equals 180 degrees.
If the sum of the measures of two angles is 90∘, then the angles are complementary angles. In the images below, each pair of angles is complementary, because their measures add to 90∘. Each angle is the complement of the other.
The sum of the measures of complementary angles is 90∘.
Part a shows a 50 degree angle next to a 40 degree angle. Together, the angles form a right angle. Below the image, it reads 50 degrees plus 40 degrees equals 90 degrees. Part b shows a 60 degree angle attached to a 30 degree angle. Together, the angles form a right angle. Below the image, it reads 60 degrees plus 30 degrees equals 90 degrees.
