1. Angles and Their Measure
Advanced Geometry

2. Angles
An angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex of the angle.

3. Name the angles in the figure
Naming Angles
Name the angles in the figure

4. Question
When an angle is named using three letters, how can you identify the vertex of the angle?

5. Question
Without seeing a figure, is it possible to give another name for ∠MKG? If so, what is it? If not, why not?

6. Example
Name ∠2 in as many different ways as possible.

7. Measuring Angles
Degrees (°) are a common measurement unit for circular arcs. There are 360° in a circle! The measure of an angle is written m∠A or m∠PQR.

8. Classifying Angles

9. Example
In a coordinate plane, plot the points and sketch angle ABC. Classify the angle.
A(5,-1), B(3,-2), C(4,-4)
A(-3,1), (-2,2), (-1,4)

10. Congruent Angles
Angles that have the same measure are called congruent angles.

11. Use a protractor to draw an angle with the given measure.
Draw an angle with a measure of 53°.

12. Use a protractor to draw an angle with the given measure.
Draw an angle with a measure of 138°.

13. Measuring Given Angles.
Measure the two angles on the sheet given to you.

14. Two angles are adjacent angles if they share a common vertex and side, but have no common interior points

15. Angle Addition Postulate
If B is in the interior of AOC, then Thus, the measure of the bigger angle is the sum of the measure of the two smaller ones

16. Angle Addition Postulate

17. Using Angle Addition Postulate
Find the measure of angle DAB
2. Find the measure of angle CAB

18. A lawn is watered by a sprinkler that has two fixed spray heads that each spray water in a fan shape. The angle that determines each of the fan shapes is The shaded area in the diagram shows where the two fan shapes overlap. Find the measure of angle 2 30 30 1 2 3