14.2. Degrees. Example 1 Use fractional parts to find. Unlock the Problem. Math Talk. Essential Question. Name
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1 ? Name. Essential Question Degrees How are degrees related to fractional parts of a circle? Geometry and Measurement.7.B Also.7.A MATHEMATICAL PROCESSES..A,..F,..G Connect You can use what you know about angles and fractional parts of a circle to understand angle measurement. Angles are measured in units called degrees. Think of a circle divided into equal parts. An angle that cuts out of the circle measures degree( ). Math Idea An angle that cuts n out of a circle measures n degrees. Unlock the Problem The angle between two spokes on the bicycle wheel cuts out or turns through 0 of a circle. What is the measure of the angle between the spokes? What part of an angle does a spoke represent? Example Use fractional parts to find the angle measure. Each turn measures _ degree. Ten turns measure _ degrees. So, the measure of the angle between the spokes is _. Math Talk Mathematical Processes How many degrees is the measure of an angle that turns through whole circle? Explain. Module
2 Example Find the measure of a right angle. right angle symbol Think: What fraction of a circle does a right angle cut out? _ STEP Write _ as an equivalent fraction with in the denominator. = STEP Write 0 in degrees. Think: = 6, so _ =. An angle that cuts out of a circle measures _. An angle that cuts 0 out of a circle measures _. Remember To write an equivalent fraction, multiply the numerator and denominator by the same factor. So, a right angle measures _. Share and Show. Find the measure of the angle. What fraction of the circle does the angle cut out? = Think: = 6, so _ =. So, the measure of the angle is _. Tell the measure of the angle in degrees... _ Math Talk Mathematical Processes If an angle measures 60º, what fraction of a circle does it cut out? Explain. _
3 Name Unlock the Problem. Multi-Step Ava started reading at :0 p.m. She stopped for a snack at :0 p.m. During this time, through what fraction of a circle did the minute hand turn? How many degrees did the minute hand turn? 0 0 a. What are you asked to find? b. What information can you use to find the fraction of a circle through which the minute hand turned? c. How can you use the fraction of a circle through which the minute hand turned to find how many degrees it turned? d. Show how to solve the problem. e. Complete the sentences. = From :0 p.m. to :0 p.m., the minute hand made a _ turn clockwise. The minute hand turned _ degrees.. Write Math Is this angle measure obtuse? Explain. 6. Analyze What fraction of a circle does a straight angle cut out? What is the measure of a straight angle? Explain. Module Lesson
4 Daily Assessment Task Mathematical Processes Fill in the bubble completely to show your answer. 7. What is the measure of the angle in degrees? A 0 B C D 0 0. Use Mathematical Language What type of angle is shown? A right C acute B obtuse D straight. Multi-Step A circle is divided into equal sections. An angle measures the same as the total measure of of the sections. What is the measure of the angle? A 70 C B 0 D 6 0. How many degrees are in an angle that cuts _ of a circle? A 0 º B 0 º C 70 º D º
5 Homework and Practice Name Geometry and Measurement.7.B MATHEMATICAL PROCESSES..A,..F,..G. Degrees. Find the measure of the angle. What fraction of the circle does the angle cut out? = So, the measure of the angle is _. Tell the measure of the angle in degrees Problem Solving. At 6:0 p.m., Elena left her house to walk to Claire s house. She arrived at 6: p.m. During this time, through what fraction of a circle did the minute hand turn? 0 0. How many degrees did the minute hand turn as it moved from to? 6. Suppose Elena takes a route that is minutes longer. How would this change your answers to exercises and? Explain. Module Lesson 7
6 Lesson Check TEXAS Test Prep Fill in the bubble completely to show your answer. 7. Which type of angle is shown?. What is the measure of the angle in degrees? 0 A B C D acute straight obtuse right A B 7 C D 0. How many degrees are in an angle that cuts _ of a circle? A B 0 C 0 D 0 0. What is the measure of the angle in degrees? A 0 B 0. Multi-Step Alex cut a pizza into equal slices. He removed of the slices of pizza. What is the measure of the angle made by the missing slices of pizza? A B 0 C 0 D 0 C D. Multi-Step Julia woke up at 7:0 a.m. She left for school at 7: a.m. How many degrees did the minute hand on the clock turn from the time Julia woke up to the time she left for school? A 0 B 60 C 0 D 0
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