7-2 Angles Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

Warm Up 1. Draw two points. Label one point A and the other point B. 2. Draw a line through points A and B. 3. Draw a ray with A as an endpoint and C as a point on the ray. 4. Name all the rays in your drawing. Course Angles AB, BA, and AC AB C

Problem of the Day The measure of Jack’s angle is twice that of Amy’s and half that of Nate’s. The sum of the measures of Amy’s and Trisha’s angles is equal to the sum of the measures of Jack’s and Nate’s angles. The sum of the measures of all the angles is equal to 180°. What is the measure of each student’s angle? Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°; Trisha’s angle: 75° Course Angles

Learn to name, measure, classify, estimate, and draw angles. Course Angles

Vocabulary angle vertex acute angle right angle obtuse angle straight angle Insert Lesson Title Here Course Angles

Course Angles An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex. Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol ° to show degrees: 90° means “90 degrees.”

Course Angles An acute angle measures less than 90°. A right angle measures exactly 90°.

Course Angles An obtuse angle measures more than 90° and less than 180°. A straight angle measures exactly 180°.

Course Angles Additional Example 1: Measuring an Angle with a Protractor Use a protractor to measure the angle. Tell what type of angle it is. Place the center point of the protractor on the vertex of the angle. G H F

Course Angles Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. Place the protractor so that ray GH passes through the 0° mark. G H F

Course Angles Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. G H F

Course Angles The measure of FGH is 120°. Write this as m FGH = 120°. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. G H F

Course Angles Since 120° > 90° and 120° < 180°, the angle is obtuse. Additional Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. G H F

Course Angles Try This: Example 1 Use a protractor to measure the angle. Tell what type of angle it is. H I G Place the center point of the protractor on the vertex of the angle.

Course Angles Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. Place the protractor so that ray HI passes through the 0° mark. H I G

Course Angles Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. H I G Using the scale that starts with 0° along ray HI, read the measure where ray HI crosses.

Course Angles Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. H I G The measure of GHI is 70°. Write this as m GHI = 70°.

Course Angles Try This: Example 1 Continued Use a protractor to measure the angle. Tell what type of angle it is. H I G Since 70° < 90°, the angle is acute.

Course Angles Additional Example 2: Drawing an Angle with a Protractor Use a protractor to draw an angle that measures 80°. Draw a ray on a sheet of paper.

Course Angles Additional Example 2 Continued Use a protractor to draw an angle that measures 80°. Place the center point of the protractor on the endpoint of the ray. Place the protractor so that the ray passes through the 0° mark.

Course Angles Additional Example 2 Continued Use a protractor to draw an angle that measures 80°. Make a mark at 80° above the scale on the protractor. Use a straightedge to draw a ray from the endpoint of the first ray through the mark you make at 80°.

Course Angles Try This: Example 2 Use a protractor to draw an angle that measures 45°. Draw a ray on a sheet of paper.

Course Angles Place the center point of the protractor on the endpoint of the ray. Place the protractor so that the ray passes through the 0° mark. Try This: Example 2 Continued Use a protractor to draw an angle that measures 45°.

Course Angles Make a mark at 45° above the scale on the protractor. Use a straightedge to draw a ray from the endpoint of the first ray through the mark you make at 45°. Try This: Example 2 Continued Use a protractor to draw an angle that measures 45°.

Course Angles To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.

Course Angles Additional Example 3: Estimating Angle Measures Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate. Think: The measure of the angle is about halfway between 90° and 180°. A good estimate would be 135°. The angle measures 131°, so the estimate is reasonable.

Course Angles Try This: Example 3 Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate. Think: The measure of the angle is a little more than halfway between 0° and 90°. A good estimate would be 50°. The angle measures 52°, so the estimate is reasonable.

Lesson Quiz Use a protractor to draw an angle with the given measure. Tell what type of angle it is ° 2. 20° 3. Draw a right angle. 4. Is the angle shown closer to 30° or 120°? acute obtuse Insert Lesson Title Here 30° Course Angles