Main Idea/Vocabulary vertical angles complementary angles supplementary angles perpendicular lines parallel lines transversal Identify special pairs of angles and relationships of angles formed by two parallel lines cut by a transversal. interior angles exterior angles alternate interior angles alternate exterior angles corresponding angles
Example 1 Find a Missing Angle Measure The two angles below are supplementary. Find the value of x x = 180 Write an equation. Answer: 25 Subtract 155 from each side. Simplify. =
1.A 2.B 3.C 4.D Example 1 A.35B.40 C.45D.50 The two angles below are complementary. Find the value of x.
Example 2 Find a Missing Angle Measure Use the two vertical angles to solve for x. Answer: x = 90Write an equation. Find the value of x in the figure. – 68 =– 68Subtract 68 from each side. x = 22Simplify.
1.A 2.B 3.C 4.D Example 2 A.20B.25 C.30D.70 Find the value of x in the figure.
Example 3 BRIDGES The drawing shows a simple bridge design. The top beam and the floor of the bridge are parallel. If 2 3 and m 3 = 55 , classify the relationship between 1 and 5. Then find m 1 and m 5. Since 3 and 5 are alternate interior angles, they are congruent. Also, since 1 and 2 are supplementary, 1 and 3 are supplementary, and 1 and 5 are supplementary. Find an Angle Measure
Example 3 Since m 3 = 55 and 2 3, m 2 = 55 . Answer: They are supplementary; m 1 = 125° and m 5 = 55°. Find an Angle Measure Since 3 and 5 are alternate interior angles, m 5 = 55 . Since 1 and 2 are supplementary, the sum of their measures is 180 . Therefore, m 1 = 180 − 55 or 125 .
1.A 2.B 3.C 4.D Example 3 A.85°B.95° C.100°D.105° BRIDGES The sketch below shows a simple bridge design. The top beam and floor of the bridge are parallel. If m 1 = 45° and m 3 = 40°, find m 4.
1.A 2.B 3.C 4.D Five Minute Check 1 A.0.035% B.0.35% C.3.5% D.35% Write 7 out of 20 as a percent. (over Chapter 5)
1.A 2.B 3.C 4.D Five Minute Check 2 Express 48% as a fraction in simplest form. (over Chapter 5) A. B. C. D.
1.A 2.B 3.C 4.D Five Minute Check 3 A.1 B.9 C.10 D is 95% of what number? (over Chapter 5)
1.A 2.B 3.C 4.D Five Minute Check 4 A.20%; decrease B.20%; increase C.16.7%; decrease D.16.7%; increase Find the percent of change from 15 to 18. State whether the percent of change is an increase or a decrease. (over Chapter 5)
1.A 2.B 3.C 4.D Five Minute Check 5 A.$11.70/pound B.$3/pound C.$2.70/pound D.$1.17/pound A grocery store manager prices items 30% above their cost. If the manager pays $0.90 per pound for strawberries, what price will he put on the strawberries? (over Chapter 5)
1.A 2.B 3.C 4.D Five Minute Check 6 A.$19.74 B.$20.20 C.$ D.$ Susan deposited $210 to open a savings account that pays 4.7% simple interest annually. If there are no other deposits or withdrawals from the account, how much will be in the account in 24 months? (over Chapter 5)