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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. • perpendicular lines Lines that intersect to form right angles • vertical angles Two pairs of opposite angles formed by two intersecting lines. The angles are congruent. • adjacent angles Two angles that have the same vertex, • share a common side, and do not overlap complementary Two angles whose sum is 90° angles • supplementary anglesTwo angles whose sum is 180° • parallel lines Two lines in a same plane that do not intersect • transversal A line that intersects two parallel lines to form eight angles • alternate interior angles • alternate exterior 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. • corresponding angles Angles that have the same position on two different parallel lines cut by a transversal. These angles are congruent. 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°. Find a Missing Angle Measure B. If ma = 53°, what is the measure of b? mb + 53 = 90 mb + 53 – 53 = 90 – 53 mb = 37 Answer: mb = 37° Write the equation. Subtract 53 from each side. Simplify. A. Elisa is cutting a piece of fabric. What is the relationship between a and b? a b A. They are complementary. B. They are supplementary. C. They are congruent. D. They are obtuse. A. B. C. D. A B C D B. If ma = 40°, what is mb? A. 140° a b B. 220° C. 50° D. 90° A. B. C. D. A B C D Find Measures of Angles Formed by Parallel Lines A. Classify the relationship between 9 and 13. Answer: Since 9 and 13 are corresponding angles, they are congruent. Find Measures of Angles Formed by Parallel Lines B. If m13 is 75°, find m11 and m15. Since 13 and 11 are alternate interior angles, they are congruent. So, m11 = 75°. 11 and 15 are corresponding angles and are congruent. So, m15 = 75°. Answer: m11 = 75° and m15 = 75° A. What is the relationship between 1 and 5? 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. B. C. D. A B C D B. If m3 = 78°, what is m7? A. 12° B. 22° C. 78° D. 102° A. B. C. D. A B C D Use Algebra to Find Missing Angle Measures ALGEBRA Angles DEF and WXY are complementary angles, with mDEF = 2x and mWXY = 3x – 20. Find the measures of DEF and WXY. Step 1 Find the value of x. mDEF + mWXY = 90 2x + 3x – 20 = 90 Complementary angles Replace mDEF with 2x and mWXY with 3x – 20. Use Algebra to Find Missing Angle Measures Combine like terms. Add 20 to each side. Simplify. Divide each side by 5. Simplify. Use Algebra to Find Missing Angle Measures Step 2 Replace x with 22 to find the measure of each angle. mDEF = 2x = 2(22) or 44 mWXY = 3x – 20 = 3(22) – 20 or 46 Answer: mDEF = 44° and mWXY = 46° Angles RST and ABC are complementary angles with mRST = 3x and mABC = x + 10. What are the measures of ABC and RST? A. mABC = 12° and mRST = 78° B. mABC = 20° and mRST = 70° C. mABC = 30° and mRST = 60° D. mABC = 30° and mRST = 70° A. B. C. D. A B C D