1. Ray-- A part of a line that extends indefinitely in one direction from a fixed point.
Opposite rays-- Two rays that are part of the same line and have only their endpoints in common. In the figure, 𝑌𝑋  and  𝑌𝑍  are opposite rays.
Vocabulary

2. Side--The two rays that form an angle.
Angle-- A figure formed by two rays with a common endpoint. In the figure, ∠RST is formed by  𝑆𝑅  and  𝑆𝑇   with the common endpoint (or vertex) S.
Side--The two rays that form an angle.
Vertex--The common endpoint of the rays forming the angle.
Vocabulary

3. A. Name all angles that have B as a vertex.
Angles and Their Parts
A. Name all angles that have B as a vertex.
Answer:
Example 1

4. Angles and Their Parts
B. Name the sides of 5.
Answer:
Example 1

5. Angles and Their Parts C.
Example 1

6. A. A. B. C. D. A B C D
Example 1a

7. B. A. B. C.
D. none of these A B C D
Example 1b

8. A B C D Which of the following is another name for 3? C. A. B. C. D.
Example 1c

9. Degreee--The most common unit of measure for angles
Degreee--The most common unit of measure for angles. If a circle were divided into 360 equal-sized parts, each part would have an angle measure of 1 degree, denoted as 1°.
Concept

10. A. Measure TYV and classify it as right, acute, or obtuse.
Measure and Classify Angles
A. Measure TYV and classify it as right, acute, or obtuse.
Answer: mTYV = 90, so TYV is a right angle.
Example 2

11. Answer: 180 > mWYT > 90, so WYT is an obtuse angle.
Measure and Classify Angles
Answer: 180 > mWYT > 90, so WYT is an obtuse angle.
Example 2

12. Measure and Classify Angles
Example 2

13. A B C D A. Measure CZD and classify it as right, acute, or obtuse.
A. 30°, acute
B. 30°, obtuse
C. 150°, acute
D. 150°, obtuse A B C D
Example 2a

14. A B C D B. Measure CZE and classify it as right, acute, or obtuse.
A. 60°, acute
B. 90°, acute
C. 90°, right
D. 90°, obtuse A B C D
Example 2b

15. A B C D C. Measure DZX and classify it as right, acute, or obtuse.
A. 30°, acute
B. 30°, obtuse
C. 150°, acute
D. 150°, obtuse A B C D
Example 2c

16. Bisect--To separate something into two congruent parts.
Bisect an angle
Bisect--To separate something into two congruent parts.
Vocabulary

17. Measure and Classify Angles
INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find mGBH and mHCI if GBH  HCI, mGBH = 2x + 5, and mHCI = 3x – 10.
Example 3

18. mGBH  mHCI Definition of congruent angles
Measure and Classify Angles
Step 1 Solve for x.
GBH  HCI Given
mGBH  mHCI Definition of congruent angles
2x + 5 = 3x – 10 Substitution
2x + 15 = 3x Add 10 to each side.
15 = x Subtract 2x from each side.
Example 3

19. Step 2 Use the value of x to find the measure of either angle.
Measure and Classify Angles
Step 2 Use the value of x to find the measure of either angle. .
Answer: mGBH = 35, mHCI = 35
Example 3

20. Find mBHC and mDJE if BHC  DJE, mBHC = 4x + 5, and mDJE = 3x + 30.
A. mBHC = 105, mDJE = 105
B. mBHC = 35, mDJE = 35
C. mBHC = 35, mDJE = 105
D. mBHC = 105, mDJE = 35 A B C D
Example 3