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

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

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

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

Angles and Their Parts C. Example 1

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

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

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

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

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

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

Measure and Classify Angles Example 2

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

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

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

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

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

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

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

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