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Then/Now You have learned about angles before (previous course) Examine relationships between pairs of angles. Examine relationships of angles formed by parallel lines and a transversal.

Vocabulary perpendicular lines vertical angles adjacent angles complementary angles supplementary angles parallel lines Lines that intersect to form right angles Two pairs of opposite angles formed by two intersecting lines. The angles are congruent. Two angles that have the same vertex, share a common side, and do not overlap Two angles whose sum is 90° Two angles whose sum is 180° Two lines in a same plane that do not intersect

Vocabulary transversal alternate interior angles alternate exterior angles corresponding angles A line that intersects two parallel lines to form eight angles Nonadjacent interior angles found on opposite sides of the transversal. In parallel lines, these are congruent. Nonadjacent exterior angles found on opposite sides of the transversal. In parallel lines, these are congruent. Angles that have the same position on two different parallel lines cut by a transversal. These angles are congruent.

Concept A

Example 1 A Find a Missing Angle Measure A. Jun is cutting a tile. Classify the relationship of  a and  b. Answer: The angles are complementary. The sum of their measures is 90°.

Example 1 B Find a Missing Angle Measure B. If m  a = 53°, what is the measure of  b? m  b + 53 = 90Write the equation. m  b + 53 – 53 = 90 – 53Subtract 53 from each side. m  b = 37Simplify. Answer: m  b = 37°

A.A B.B C.C D.D Example 1 CYP A A.They are complementary. B.They are supplementary. C.They are congruent. D.They are obtuse. A. Elisa is cutting a piece of fabric. What is the relationship between  a and  b? a b

A.A B.B C.C D.D Example 1 CYP B A.140° B.220° C.50° D.90° B. If m  a = 40°, what is m  b? a b

Concept B

Example 2 A Find Measures of Angles Formed by Parallel Lines Answer: Since  9 and  13 are corresponding angles, they are congruent. A. Classify the relationship between  9 and  13.

Example 2 Find Measures of Angles Formed by Parallel Lines Answer: m  11 = 75° and m  15 = 75° B. If m  13 is 75°, find m  11 and m  15. Since  13 and  11 are alternate interior angles, they are congruent. So, m  11 = 75°.  11 and  15 are corresponding angles and are congruent. So, m  15 = 75°.

A.A B.B C.C D.D Example 2 CYP A A.They are corresponding and congruent. B.They are adjacent and supplementary. C.They are corresponding and supplementary. D.They are adjacent and congruent. A. What is the relationship between  1 and  5?

A.A B.B C.C D.D Example 2 CYP B A.12° B.22° C.78° D.102° B. If m  3 = 78°, what is m  7?

Example 3 Use Algebra to Find Missing Angle Measures ALGEBRA Angles DEF and WXY are complementary angles, with m  DEF = 2x and m  WXY = 3x – 20. Find the measures of  DEF and  WXY. m  DEF + m  WXY = 90Complementary angles 2x + 3x – 20 = 90Replace m  DEF with 2x and m  WXY with 3x – 20. Step 1 Find the value of x.

Example 3 Use Algebra to Find Missing Angle Measures Combine like terms. Add 20 to each side. Simplify. Divide each side by 5. Simplify.

Example 3 Use Algebra to Find Missing Angle Measures Answer: m  DEF = 44° and m  WXY = 46° Step 2 Replace x with 22 to find the measure of each angle. m  DEF = 2xm  WXY = 3x – 20 = 2(22) or 44 = 3(22) – 20 or 46

A.A B.B C.C D.D Example 3 A.m  ABC = 12° and m  RST = 78° B.m  ABC = 20° and m  RST = 70° C.m  ABC = 30° and m  RST = 60° D.m  ABC = 30° and m  RST = 70° Angles RST and ABC are complementary angles with m  RST = 3x and m  ABC = x What are the measures of  ABC and  RST?

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