Write an equation and solve for x, then find the missing angle measures. Pictures are not drawn to scale. 1. Equation: Solution: Equation: Solution:
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1 6.1d Class Activity: Triangles and Circles In chapter 5, you worked with angle measures in triangles. Now, you are going to practice writing equations to solve for a missing angle measure. Recall from Chapter 5 that the angles of a triangle sum to 180 o. Example: Find the missing angle measure: x = x = x = 36 o Sometimes, x is not the missing angle measure: 2x = 180 2x = x = x = 37 However, x is not the missing angle measure. 2x is, so the missing angle measure is 2(37 o ) = 74 o Write an equation and solve for x, then find the missing angle measures. Pictures are not drawn to scale WB6-28
2 5. One angle of a triangle is 5 times the smallest angle. The other angle is The sum of 2 angles of a triangle is 37. What is the measure of the other angle? 7. The ratio of angles of a triangle is 3:2:1. What are the angle measurements? 9. The ratio of the angles of a triangle is 5:2/3:1. What are the measures of all three angles? 8. One of the angles of a triangle is one-fourth the size of the largest angle. The other angle is one-half the size of the largest angle. What are the measures of all the angles? 10. One angle of a triangle is 63. The ratio of the other two angles is 5:2. What are the measures of all the angles of the triangle? 11. The angle of a triangle is 54. The ratio of the other two angles is 3:5. What are the measurements of all the triangles. 12. Two angles of a right triangle have the ratio 5:7. What are the measures of the angles? Now for circles: Review: What is the formula for the Circumference of a circle? What is the formula for the Area of a circle? 13. What if you were only given the circumference? Could you find the radius or diameter? 7WB6-29
3 14. Michael loves swimming. He swam around the edge of a circular pool and found that it took him 176 strokes to swim one complete time around the pool. About how many strokes will it take him to swim across the pool? (Use 3.14 for pi) 15. The circumference of the center circle of a soccer field is yards. What is the radius of the circle? 16. Find the radius of a circle with a circumference of 22 feet. 17. A farmer has a 100 feet x 100 feet plot of land he needs to water. He has a sprinkler that waters in a circle. The sprinkler has a reach of 50 feet. If he puts the sprinkler in the center of the plot of land, what percent of the plot will be watered? (Hint: Draw a picture first) 18. Pizzas are sold according to diameter. For example, a 6 inch pizza is a pizza with a diameter of 6 inches. At Francesco s pizzeria, there are two pizzas. Pizza A is a 12 inch, and Pizza B has an area of 450 in 2. Which pizza is bigger? What is the percent of increase from the smaller pizza to the larger pizza? 19. A bike s wheel diameter is 50 cm. If the wheel rotates 45 times a minute, how far has the bike traveled after 30 minutes? 20. Mary has a circular table whose diameter is 7 feet. She would like to put a tablecloth on it, but the packaging only gives the area. The tablecloth she bought says it is 110 ft 2. Will the tablecloth fit? 7WB6-30
4 6.1d Homework: Triangles and Circles Write an equation to find x, then find the measure of the missing angle. Pictures are not drawn to scale WB6-31
5 7. One angle of a triangle is 3 times the smallest angle. The third angle is The sum of 2 angles of a triangle is 39. What is the measure of the other angle? = x 9. One angle of a triangle has a measure of x. Another angle is 3 times the size of angle x. The third angle is half the size of angle x. What are the measures of all three angles? 10. One of the angles of a triangle is three-fourths the size of the largest angle. The other angle is onehalf the size of the largest angle. What are the measures of all the angles? 11. The ratio of angles of a triangle is 3:1:1. What are the angle measurements? 12. One angle of a triangle is 80. The ratio of the other two angles is 3:2. What are the measures of all the angles of the triangle? 13. The angle of a triangle is 52. The ratio of the other two angles is 3:4. What are the measurements of all the triangles. 14. Two angles of a right triangle have the ratio 2:3. What are the measures of the angles? 7WB6-32
6 15. Phil has a lamp with a circular base that he would like to fit onto a circular side table in his house. The area of the base of the lamp is 70 in 2. The table has a radius of 5 in. Will the lamp fit? Be sure to show all your work. 16. The circumference of a pizza is 81 in. What is the radius? 17. The circumference of a circular hot tub cover is 200 ft. What is the area of the cover? 18. The circumference of a basketball hoop is in. What is the area inside the hoop? 19. A pizza place charges $12 for a 12 inch pizza, $14 for a 14 inch pizza, $16 for a 16 inch pizza, and $20 for a 20 inch pizza. Which pizza is the best deal? Justify your response. 7WB6-33
7 Spiral Review 1. Luis went to a soccer game with some friends. He bought two sodas for $1.50 each and four giant candy bars for $2.25 each. Write a numeric expression showing how much he spent. Then calculate the total he spent. 2. Use long division to show how you can convert this fraction to a decimal and then a percent 3. Solve: = 4. Simplify: x + 3x 7x + 2x 2 5. Write a context for the following expression: 4(x 3) 7WB6-34
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