1. 1.6 Angles and Their Measures

2. Angle
An angle consists of two different rays that have the same endpoint. The rays are the sides of the angle. The initial point is the vertex of the angle.
The angle that has sides AB and AC is denoted by BAC, CAB, A. The point A is the vertex of the angle. A B C
Vertex
Sides

4. Ex.1: Naming Angles Name the angles in the figure: SOLUTION:Q S P
Name the angles in the figure:
SOLUTION:
There are three different angles.
PQS or SQP
SQR or RQS
PQR or RQP R
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.

5. Note:
The measure of A is denoted by mA. The measure of an angle can be approximated using a protractor, using units called degrees(°).
For instance, BAC has a measure of °, which can be written as mBAC = 50°. B A C

6. more . . .
Angles that have the same measure are called congruent angles.

7. Note – Equal & Congruent are not exactly the same!!!
MEASURES ARE EQUAL
mBAC = mDEF
ANGLES ARE CONGRUENT
BAC  DEF
“is congruent to”
“is equal to”

8. Classifying Angles
Angles are classified as acute, right, obtuse, and straight, according to their measures. Angles have measures greater than 0° and less than or equal to 180°.

9. Interior/Exterior
A point is in the interior of an angle if it is between points that lie on each side of the angle.
A point is in the exterior of an angle if it is not on the angle or in its interior.

10. Postulate 6: Angle Addition Postulate
If P is in the interior of RST, then
mRSP + mPST = mRST S T P R