1. 1.4 What you should learn Why you should learn it
Angles and Their Measures
What you should learn
GOAL 1
Use Angle Postulates
GOAL 2
Classify angles as acute, right, obtuse, or straight.
Why you should learn it
To solve real-life problems about angles, such as the field of vision of a horse wearing blinkers.

2. 1.4 Angles and Their Measures 1 GOAL USING ANGLE POSTULATES
An _____ consists of two different rays that have the same initial point.
angle
The rays are the _____ of the angle and the initial point is the ______.
sides
vertex
The three names for this angle are A C B
The sides are
The vertex is point A.

3. Extra Example 1 Did you study Example 1???
Name the angles in the figure. M N O P
Click for the answers.
should not be used to name any angle in the figure. Why not? 1. 2. 3.
All three angles have N as the vertex, so could mean any of the angles.

4. Measuring Angles The expression is read as “the ________ of angle A.”
measure
IMPORTANT!!! Note the difference in notation between an angle and its measure. Always use the correct notation!!!
The tool used to measure angles is called a _________.
protractor
The units used to measure angles are called _______, and the symbol for them is a _.
degrees

5. Measuring Angles Q R S Let’s measure some angles. Y M T
Since we say that the angles are _________.
congruent
Remember: Angles are congruent, measures are equal.
Incorrect:
Correct:
and

6. PROTRACTOR POSTULATE
For any point A on one side of , can be matched one to one with the real numbers from 0 to ___.
180
The absolute value of the difference between the real numbers for is the ________ of
measure
Check your understanding of the Protractor Postulate by finding Use either scale on the protractor to find it, but use the same one for both rays. B O A
Click to see two solutions. or

7. To understand the next postulate, you must understand some vocabulary:
A point that is between points that lie on each side of an angle is in the _______ of the angle.
A point that is not on an angle or in its interior is in the ________ of the angle.
interior
exterior
exterior B
interior A Z
In the above diagram, A is in the interior of the angle and B is in the exterior of the angle.

8. ANGLE ADDITION POSTULATE
If P is in the interior of
then R T P S
Does it make sense? Study the figure
to be sure you understand before going on!
EXAMPLE 2

9. What is the measure of the angle that is shaded green?
Extra Example 2
The backyard of a house is illuminated by a light fixture that has two bulbs. Each bulb illuminates an angle of 120°. If the angle illuminated only by the right bulb is 35°, what is the angle illuminated by both bulbs?
Click for a picture.
What is the measure of the angle that is shaded green?
120°
Click for the solution.
120°
120°
- 35° =
85°
85°
Do you see the application of the Angle Addition Postulate?
35°

10. Checkpoint D Name the angles in the figure. Click for the solution. C
In the figure above, and
Find the measure of Click for the solution.

11. 1.4 Angles and Their Measures 2 GOAL CLASSIFYING ANGLES
We can classify all angles by their measure as follows:
Angles with measures between 0 and 90 degrees: _____
90 degree angles: _____
Angles with measures between 90 and 180 degrees: ______
180 degree angles: _______
acute
right
obtuse
straight

12. Can you match each angle with its description?
Click to check your answer. A
Important!!! Anytime this box appears at the vertex of an angle, it means that the angle is a right angle. You MUST use it when you want to show a right angle.
acute:
right:
obtuse:
straight: A A A
EXAMPLE 3

13. Extra Example 3
Plot the points A(-3, -1), B(-1, 1), C(2, 4), D(2, 1), and E(2, -2).
Then measure and classify the following angles as acute, right, obtuse, or straight. Click for each answer. a. b. c. d.
45°, acute
90°, right
180°, straight
135°, obtuse
Reminder: Be sure you understand the material before going on to the next slide. If you need to review, do so NOW!

14. The common vertex is __ and the common side is ___.
Two angles that share a common vertex and side, but have no common interior points, are called ________ angles.
adjacent A B C D
Name the two adjacent angles in the diagram. Click to check.
The common vertex is __ and the common side is ___. D
EXAMPLE 4

15. Extra Example 4 Use a protractor to draw two adjacent angles and
so that is acute and is straight.
Click to see a sample answer. L N M O
Classify as acute, right, obtuse, or straight:
obtuse

16. Does your solution meet the requirements above?
Checkpoint
Draw 5 points A, B, C, D, and E so that all four statements are true:
are adjacent.
is obtuse.
D is in the exterior of
is a right angle.
Click to see a sample answer. B C E A D
Does your solution meet the requirements above?

17. QUESTIONS?