Measuring Angles and Circle Graphs

Transcription

1 Name: Period: Date: 11 th Grade Mathematics PSSA Preparation Program o Mastered On: Measuring Angles and Circle Graphs Anchors Addressed M11.B Measure and/or compare angles in degrees (up to 360 ) (Protractors must be provided or drawn.) M11.E Estimate or calculate to make predictions based on a circle, line, bar graph, or given situation. Concepts Protractors are used to accurately measure and draw angles. Angles appear in everything from buildings to circle graphs. Angles are labeled by the points located on the rays and vertex of the angle. Recall the vertex is the point where the two rays meet and the rays form the sides of the angles. Acute angles have measures that are less than 90 degrees and obtuse angles have measures that are greater than 90 degrees. Measuring Angles with a Protractor To measure an angle with a protractor, follow these steps. STEP 1: Align the bottom line of the angle with the 0 degree line of the protractor. STEP 2: Align the vertex of the angle with the mark at the center of the protractor. STEP 3: Read the angle on the protractor where the second ray of the angle crosses the protractor s outer edge. If the angle is acute, like the one shown, the angle is the smaller number. If the angle is obtuse, the angle is the larger number. Example 1: Measure the angle shown below. Solution: Using the steps outlined above, the measure of the angle is 41.? Test Taking Tip: You can always determine whether an angle is acute or obtuse when taking a test without using a protractor. The corner of a sheet of paper forms a 90 angle. Place a the corner of the paper at the vertex and align one ray of the angle with one edge of the paper. If you can see the other ray, the angle is obtuse, otherwise the angle is acute.

2 Drawing an Angle To draw an angle given a specified measure, first draw a ray. Then, place the protractor over the vertex (endpoint of the ray). Place a small dot next to the mark on protractor that represents the desired angle and then connect the vertex to the dot to create the second ray. Verify your answer is correct by re- measuring the angle you created. Pie (Circle) Charts Pie charts are circles that are divided into wedges that represent data. Pie charts can be misleading if the percentages they represent do not equal 100%. Therefore, pie charts can only be used to display certain data. To determine the relationship between the angle and the percent it represents, the following proportion is used: percent 100 = angle 360 Example 1: According to the circle graph, what percent of students chose math as their favorite subject? Solution: Measuring the angle that represents Math. This angle is 61. Therefore, the proportion to find the percent is: Other Math x 100 = English Solving the proportion yields x = 16.9% Science Example 2: If 250 students were surveyed, how many students chose history as their favorite class? History Solution: Like the previous example, measure the angle using a protractor, then substitute the angle into the proportion: x 100 = Solving the proportion for x, x = 21.9%. Use a second proportion to determine the number of students who chose history given the percentage = x 250 Solving this proportion yields the number of students who chose history: 55 students.

3 Exercises A. Use the protractor and angles below to answer questions 1-5. Use the protractor above to measure the following angles. 1. m AOB = A. 65 B. 75 C. 115 D m EOC = A. 110 B. 180 C. 70 D m BOC = A. 65 B. 75 C. 115 D m COD = B. 20 B. 70 C. 50 D m BOD = B. 65 B. 95 C. 160 D. 125

4 B. Measure the following angles using a protractor. 6. m A = 10. m E = 7. m B = 11. m F = 8. m C = 12. m G = 9. m D = 13. m H =

5 C. Use a protractor to draw and label the following angles in the box below. Do not let the angles overlap each other. Use an additional sheet of paper is you need more room. A = 55 B = 42 C = 124 D = 20 E = 90 F = 135 G = 58 H = 173 I = 85 J = 112 K = 4 L = 176 M = 228 N = 270 O =

6 D. Use the circle charts provided to answer the questions that follow. The circle chart below shows the type of fruit that people prefer for lunch. Pear Orange Plum Peach Apple 15. Determine the angle and percent for each of the types of fruit. Fruit Angle Percent Apple Orange Peach Pear Plum 16. If 300 people were surveyed, how many people preferred peaches?

7 17. If 450 people were surveyed, how many more people preferred apples over pears? 18. Why do some of the number of people have a decimal as part of the answer? Does this mean that there is a mistake? Explain why. 19. If the survey represents ! people, how many people prefer oranges? 20. You run a bodega that has a small refrigerated section that includes sandwiches and other lunch items. There is a small amount of space left for fruit so you can only choose two types. According to the data, which types should you choose? Why?

8 E. Create a circle chart to represent your classmates responses to the following question. Record your classmates answers in the boxes below. Ask between 12 and 30 people. Which do you prefer: M&M s, Skittles, or Hershey Kisses? M&Ms Skittles Hershey Kisses 21. Calculate the percent and angle that represents each of the categories. Show your work. 22. Create and label a circle graph that represents your data using the circle below.