527 5.1 Angles In Figure 5, we use the Greek letter U (theta)* to name each angle. The table in the margin lists the upper- and lowercase Greek letters, which are often used in trigonometry. The Greek Letters Α a alpha Β b beta Γ g gamma Δ d delta Ε e epsilon Ζ z zeta Η h eta ϴ u theta Ι i iota Κ k kappa Λ l lambda Μ m mu Ν n nu Ξ j xi Ο o omicron Π p pi Ρ r rho Σ s sigma Τ t tau Υ y upsilon Φ f phi Χ x chi Ψ c psi Ω v omega If the sum of the measures of two positive angles is 90°, the angles are complementary and the angles are complements of each other. Two positive angles with measures whose sum is 180° are supplementary, and the angles are supplements. EXAMPLE 1 Finding the Complement and the Supplement of an Angle Find the measure of (a) the complement and (b) the supplement of an angle measuring 40°. SOLUTION (a) To find the measure of its complement, subtract the measure of the angle from 90°. 90° - 40° = 50° Complement of 40° (b) To find the measure of its supplement, subtract the measure of the angle from 180°. 180° - 40° = 140° Supplement of 40° S Now Try Exercise 11. EXAMPLE 2 Finding Measures of Complementary and Supplementary Angles Find the measure of each marked angle in Figure 6. SOLUTION (a) Because the two angles in Figure 6(a) form a right angle, they are complementary angles. 6x + 3x = 90 Complementary angles sum to 90°. 9x = 90 Combine like terms. x = 10 Divide by 9. Be sure to determine the measure of each angle by substituting 10 for x in 6x and 3x. The two angles have measures of 61102 = 60° and 31102 = 30°. (b) The angles in Figure 6(b) are supplementary, so their sum must be 180°. 4x + 6x = 180 Supplementary angles sum to 180°. 10x = 180 Combine like terms. x = 18 Divide by 10. The angle measures are 4x = 41182 = 72° and 6x = 61182 = 108°. S Now Try Exercises 23 and 25. Don’t stop here. *In addition to u (theta), other Greek letters such as a (alpha) and b (beta) are used to name angles. (6x)° (3x)° (a) Figure 6 (4x)° (6x)° (b) Acute angle 0°< u < 90° u Right angle u = 90° u Obtuse angle 90°< u < 180° u Straight angle u = 180° u Figure 5
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