Angles and Their Measures

Angles An angle consists of two different rays that share a point. The rays are the sides of the angle. The point shared is the vertex of the angle. There are 3 ways to write an angle:  BAC,  CAB,  A. The point A is the vertex of the angle.

Naming Angles Name the angles in the figure: SOLUTION: There are three different angles.  PQS or  SQP  SQR or  RQS  PQR or  RQP You should not name any of these angles as  Q because all three angles have Q as their vertex. The name  Q would not distinguish one angle from the others.

Classifying Angles Angles are classified as acute, right, obtuse, and straight. 0º to 89º 90º 91º to 179º 180º

Note:  BAC has a measure of 50°, which can be written as m  BAC = 50°. B A C B C B C B A C B

more... Angles that have the same measure are called congruent angles. 50 ° E F D

Intersecting Lines Create angle relationships When given the measure of one angle, you can determine the other angles by the relationships formed

Vertical Angles Formed when two lines intersect Across the vertex from each other Congruent – have the same measure  What is  1’s vertical angle?  If  1 = 75 ⁰, what else do you know?

Adjacent Angles Have a common side and vertex Side-by-side –Which angle is adjacent to  1?

Complementary Angles Complementary angles –Adjacent –acute angles that add up to 90º (right angle). For example: If I tell you that 2 angles are complementary and one angle measures 46º, what is the measure of the other angle?

Supplementary Angles Supplementary angles –Adjacent –angles that add up to 180º (straight angle) For example: If I tell you that 2 angles are supplementary and one angle measures 125º, what is the measure of the other angle?