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NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Lesson Reading Guide Angle Measure Get Ready for the Lesson Read the introduction to Lesson 1-4 in your textbook. • A semicircle is half a circle. How many degrees are there in a semicircle? • How many degrees are there in a quarter circle? Read the Lesson Remember What You Learned 3. A good way to remember related geometric ideas is to compare them and see how they are alike and how they are different. Give some similarities and differences between congruent segments and congruent angles. Chapter 1 28 Glencoe Geometry Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 1. Match each description in the first column with one of the terms in the second column. Some terms in the second column may be used more than once or not at all. a. a figure made up of two noncollinear rays with a 1. vertex common endpoint 2. angle bisector b. angles whose degree measures are less than 90 3. opposite rays c. angles that have the same measure 4. angle d. angles whose degree measures are between 90 and 180 5. obtuse angles e. a tool used to measure angles 6. congruent angles f. the common endpoint of the rays that form an angle 7. right angles g. a ray that divides an angle into two congruent angles 8. acute angles 9. compass 10. protractor 2. Use the figure to name each of the following. E a. a right angle F D b. an obtuse angle 28⬚ 28⬚ C c. an acute angle d. a point in the interior of ⬔EBC A B G e. a point in the exterior of ⬔EBA f. the angle bisector of ⬔EBC g. a point on ⬔CBE h. the sides of ⬔ABF i. a pair of opposite rays j. the common vertex of all angles shown in the figure k. a pair of congruent angles l. the angle with the greatest measure NAME ______________________________________________ DATE 1-4 ____________ PERIOD _____ Study Guide and Intervention Angle Measure Measure Angles If two noncollinear rays have a common endpoint, they form an angle. The rays are the sides of the angle. The common endpoint is the vertex. The angle at the right can be named as ⬔A, ⬔BAC, ⬔CAB, or ⬔1. B 1 A A right angle is an angle whose measure is 90. An acute angle has measure less than 90. An obtuse angle has measure greater than 90 but less than 180. Example 1 S R 1 2 C Example 2 Measure each angle and classify it as right, acute, or obtuse. T 3 Q P E D a. Name all angles that have R as a vertex. Three angles are ⬔1, ⬔2, and ⬔3. For other angles, use three letters to name them: ⬔SRQ, ⬔PRT, and ⬔SRT. A B a. ⬔ABD Using a protractor, m⬔ABD ⫽ 50. 50 ⬍ 90, so ⬔ABD is an acute angle. b. Name the sides of ⬔1. , RP RS b. ⬔DBC Using a protractor, m⬔DBC ⫽ 115. 180 ⬎ 115 ⬎ 90, so ⬔DBC is an obtuse angle. c. ⬔EBC Using a protractor, m⬔EBC ⫽ 90. ⬔EBC is a right angle. Exercises Refer to the figure. A B 4 1. Name the vertex of ⬔4. 1 D 2. Name the sides of ⬔BDC. 3 2 C 3. Write another name for ⬔DBC. Measure each angle in the figure and classify it as right, acute, or obtuse. N M S 4. ⬔MPR P 5. ⬔RPN R 6. ⬔NPS Chapter 1 29 Glencoe Geometry Lesson 1-4 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. C NAME ______________________________________________ DATE 1-4 Study Guide and Intervention ____________ PERIOD _____ (continued) Angle Measure Congruent Angles Angles that have the same measure are congruent angles. A ray that divides an angle into two congruent angles is called an angle bisector. In the figure, PN is the angle bisector of ⬔MPR. Point N lies in the interior of ⬔MPR and ⬔MPN ⬵ ⬔NPR. M N P R Q R Example Refer to the figure above. If m⬔MPN ⫽ 2x ⫹ 14 and m⬔NPR ⫽ x ⫹ 34, find x and find m⬔MPR. Since PN bisects ⬔MPR, ⬔MPN ⬵ ⬔NPR, or m⬔MPN ⫽ m⬔NPR. 2x ⫹ 14 ⫽ x ⫹ 34 2x ⫹ 14 ⫺ x ⫽ x ⫹ 34 ⫺ x x ⫹ 14 ⫽ 34 x ⫹ 14 ⫺ 14 ⫽ 34 ⫺ 14 x ⫽ 20 m⬔NPR ⫽ (2x ⫹ 14) ⫹ (x ⫹ 34) ⫽ 54 ⫹ 54 ⫽ 108 Exercises bisects ⬔PQT, and QP and QR are opposite rays. QS 1. If m⬔PQT ⫽ 60 and m⬔PQS ⫽ 4x ⫹ 14, find the value of x. S T 2. If m⬔PQS ⫽ 3x ⫹ 13 and m⬔SQT ⫽ 6x ⫺ 2, find m⬔PQT. and BC are opposite rays, BF bisects ⬔CBE, and BA BD bisects ⬔ABE. E D 3. If m⬔EBF ⫽ 6x ⫹ 4 and m⬔CBF ⫽ 7x ⫺ 2, find m⬔EBC. F 1 A 2 3 B 4 C 4. If m⬔1 ⫽ 4x ⫹ 10 and m⬔2 ⫽ 5x, find m⬔2. 5. If m⬔2 ⫽ 6y ⫹ 2 and m⬔1 ⫽ 8y ⫺ 14, find m⬔ABE. 6. Is ⬔DBF a right angle? Explain. Chapter 1 30 Glencoe Geometry Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. P