Review > Solve each equation. 1. x+3x=180 2. (180 - x)+ (90 - x) =210 What types of special You have classified individual angles based on their : relationships exist between measures as acute, obtuse, or right. pairs of angles? @ Activity 3 7. Are all adjacent angles supplementary? Explain your reasoning. 8. Are all supplementary angles adjacent? Explain your reasoning. Activity 4 THINKING AND REASONING . Complete tasks with mathematical fluency. Linear Pairs > Let's explore a different angle relationship. WORKED EXAMPLE 21 and 42 form a linear pair. 23 and 24 do not form a linear pair. m - IN m@ Activity 4 1. Use the figures in the worked example to define a linear pair of angles in your own words. 2. Draw 22 so that it forms a linear pair with 21. Use one sheet of patty paper and record your response. Label your patty paper \"Linear Pair.\" TAKE NOTE... Two adjacent angles with noncommon sides that form a line create a linear pair of angles. @ Activity 4 3 Name all linear pairs in the figure shown. 4. When the angles that form a linear pair are congruent, what can you conclude? @ Activity 4 5 What is the difference between a linear pair of angles and supplementary angles that share a common side? 6. What is the difference between a linear pair of angles and supplementary angles that do not share a common side? 7. Angle ABC and angle CBD form a linear pair. Write and solve an equation to determine the measure of ZABC. @ Activity 4 8. The angles shown are a linear pair of angles. Solve for x. 9. If two angles form a linear pair, then the sum of the measures of the linear pair of angles is _ e THINKING AND REASONING >.\"_ Let's explore one more special angle relationship between pairs of angles. WORKED EXAMPLE 21 and 2 are vertical angles 3 and 4 are not vertical angles. = L A ASK YOURSELF... Is there another way to draw 22 so that it forms a vertical angle pair with 217 @ Activity 5 1. Use the figures in the worked example to define vertical angles in your own words. 2. Draw 22 so that it forms a vertical angle pair with 21. @ Activity 5 3. Name all vertical angle pairs in the diagram shown. 4. Trace the figure in Question 3 on two different sheets of patty paper. Be sure you number the angles. Use the patty paper to investigate the measures of vertical angles. What do you notice? TAKE NOTE... Two nonadjacent angles formed by a pair of intersecting lines are vertical angles. THINK ABOUT... How can you rotate the patty paper to investigate vertical angles? @ Activity 5 5. Use your protractor to measure each angle in Question 3. What do you notice? 6. Use what you know about supplementary angles and linear pairs to justify your investigations in Questions 4 and 5. 7. Label one sheet of your patty paper \"Vertical Angles.\" When two lines intersect to form vertical angles, the measure of each angle in a pair of vertical angles is 74 Activity 1 Supplements and Complements In the previous activity, you created supplementary angles and complementary angles. > Let's create sets of supplementary angles. 1. Use a protractor to draw a pair of supplementary angles that share a side. What is the measure of each angle? THINKING AND REASONING Complete tasks with mathematical TAKE NOTE... Two angles are supplementary angles when the sum of their angle measures is equal to 180. Two angles are complementary angles when the sum of their angle measures is equal to 90. @ Activity 5 8 Write and solve an equation to determine the measures of all four angles in each diagram. a) =20 Talk the Talk Extra Special Delivery > Determine the number of pairs of each angle relationship formed by two intersecting lines. Draw a figure to justify your response. 1. Supplementary angles Complementary angles Adjacent angles G (e Linear pairs of angles @ Talk the Talk 5. Vertical angles 6. Suppose two lines intersect and you are given the measure of one angle. Can you determine the measures of the remaining angles without using a protractor? Explain your reasoning. 7. The figure shows that the intersection of two lines forms four different angles. a) Describe the relationship between the vertical angles. b) Describe the relationship between the adjacent angles. @ Talk the Talk 8. Draw and label a diagram that includes at least one of each relationship. Then identify the angles that satisfy each description. Complementary angles @ Supplementary angles Perpendicular lines @ Adjacent angles Linear pair Vertical angles @ Activity 1 7 Given each statement, write and solve an equation to determine the measure of each angle in the angle pair. a) b) c) d) e) f) REMEMBER... Congruent angles Two angles are both congruent and supplementary. are angles that have Two angles are both congruent and complementary. the same measure. The supplement of an angle is half the measure of the angle itself. The supplement of an angle is 20 more than the measure of the angle itself. Angles 1 and 2 are complementary. The measure of angle 2 is 10 greater than the measure of angle 1. Angles 1 and 2 are supplementary. The measure of angle 1 is three degrees less than twice the measure of angle 2. \fil THINKING AND REASONING >o._ Draw and label BC1AB at point B. How many right angles do the lines form? 3. Name all angles that you know are right angles in the figure shown. Note: Points A, D, and B lie on the same line segment. C THINK ABOUT... Compare your drawings with your partner's drawings. What do you notice? TAKE NOTE... When points lie on the same line or line segment, you say they are collinear. THINKING AND REASONING Activity 3 . Complete tasks with mathematical fluency. Adjacent Angles In each of the next three activities you will explore special angle pairs. ASK YOURSELF... Are there other WORKED EXAMPLE ways to draw 42 so that it is adjacent 21 and Z2 are 23 and 24 are not adjacent angles. adjacent angles. to 41? m@ Activity 3 1. Use the figures in the worked example to define adjacent angles in your own words. 2. Draw and label 22 so that it is adjacent to 21. @ Activity 3 Adjacent angles are two angles that share a common vertex and share a common side 3. Is it possible to draw two angles that share a vertex, but are not adjacent? If so, draw an example. 4. s it possible to draw two angles that share a side, but do not share a vertex? If so, draw an example. If not, explain your reasoning. Learning Goals . Calculate the supplement and complement of an angle. . ) . ) ) KEY TERMS - Classify adjacent angles, linear pairs, and vertical angles. straight angle . Use facts about angle relationships to write and solve supplementary angles simple equations for unknown angles. iR complementary angles perpendicular collinear adjacent angles linear pair vertical angles