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Five-Minute Check (over Chapter 10) Then/Now New Vocabulary Key Concept: Pairs of Angles Example 1: Find a Missing Angle Measure Key Concept: Names of Special Angles Example 2: Find Measures of Angles Formed by Parallel Lines Example 3: Use Algebra to Find Missing Angle Measures Over Chapter 10 A. 5 B. 6 C. 7 D. 8 Over Chapter 10 Which list of numbers is correctly ordered least to greatest? A. B. C. D. Over Chapter 10 If c is the measure of the hypotenuse and a = 6 and b = 9, find the measure of c. Round to the nearest tenth. A. 10.5 units B. 10.8 units C. 11.3 units D. 12 units Over Chapter 10 Find the distance between A(–3, 4), and B(5, 2). Round to the nearest tenth. A. 8.2 units B. 8.1 units C. 8.0 units D. 7.9 units Over Chapter 10 What is the value of x? Classify the triangle by its angles and by its sides. A. 102°; obtuse scalene B. 92°; acute scalene C. 90°; right scalene D. 82°; acute scalene You have already found the missing angle measure of a triangle. (Lesson 10–3) • Examine relationships between pairs of angles. • Examine relationships of angles formed by parallel lines and a transversal. • perpendicular lines • transversal • vertical angles • alternate interior angles • adjacent angles • complementary angles • supplementary angles • parallel lines • alternate exterior angles • corresponding angles 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 A. They are complementary. B. They are supplementary. C. They are congruent. D. They are obtuse. b B. If ma = 40°, what is mb? A. 140° B. 220° C. 50° D. 90° a b 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. B. If m3 = 78°, what is m7? A. 12° B. 22° C. 78° D. 102° 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°