G.CO.C.9: Lines and Angles 3
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1 G.CO.C.9: Lines and Angles 3 1 In the accompanying diagram, line a intersects line b. 3 In the accompanying diagram, lines a and b are parallel, and lines c and d are transversals. What is the value of x? 1) 10 2) 5 3) 10 4) 90 2 In the accompanying diagram, parallel lines AB and CD are intersected by transversal at points G and H, respectively, m AGH = x + 15, and m GHD = 2x. Which angle is congruent to angle 8? 1) 6 2) 5 3) 3 4) 4 4 In the accompanying diagram, line n is parallel to line m, line t is a transversal, and m 1 = 24. Which equation can be used to find the value of x? 1) 2x = x ) 2x + x + 15 = 180 3) 2x + x + 15 = 90 4) 2x(x + 15) = 0 What does x equal, in degrees? 1) 24 2) 66 3) 114 4) 156 1
2 5 In the accompanying figure, what is one pair of alternate interior angles? 7 In the diagram below, AB is parallel to CD. Transversal EF intersects AB and CD at G and H, respectively. If m AGH = 4x and m GHD = 3x + 40, what is the value of x? 1) 1 and 2 2) 4 and 5 3) 4 and 6 4) 6 and 8 1) 20 2) 40 3) 80 4) In the accompanying diagram, line is parallel to line m, and line t is a transversal. 8 The accompanying diagram shows a football player crossing the 20-yard line at an angle of 30 and continuing along the same path. Which must be a true statement? 1) m 1 + m 4 = 180 2) m 1 + m 8 = 180 3) m 3 + m 6 = 180 4) m 2 + m 5 = 180 What is the measure of angle B, where the player crosses into the end zone? 1) 30 2) 60 3) 150 4) 180 2
3 9 The accompanying diagram shows two parallel streets, Main Street and Brooks Road, intersected by Jay Street. The obtuse angle that Jay Street forms with Brooks Road is three times the measure of the acute angle that Jay Street forms with Main Street. 11 Angle A and angle B are complementary angles. If m A = x, which expression represents the number of degrees in angle B? 1) x 180 2) 180 x 3) x 90 4) 90 x What is the measure of the acute angle formed by Jay Street and Main Street? 1) 45 2) 60 3) 90 4) The accompanying diagram shows two parallel roads, Hope Street and Grand Street, crossed by a transversal road, Broadway. 12 If the measure of an angle is represented by 2x, which expression represents the measure of its complement? 1) 180 2x 2) 90 2x 3) x 4) 88x 13 The ratio of two supplementary angles is 2:7. What is the measure of the smaller angle? 1) 10 2) 14 3) 20 4) The ratio of two supplementary angles is 3:6. What is the measure of the smaller angle? 1) 10 2) 20 3) 30 4) 60 If m 1 = 110, what is the measure of m 7? 1) 40 2) 70 3) 110 4) AB and CD intersect at point E, m AEC = 6x + 20, and m DEB = 10x. What is the value of x? 1) ) 5 3) 10 4)
4 16 The measures of two complementary angles are represented by (3x + 15) and (2x 10). What is the value of x? 1) 17 2) 19 3) 35 4) In the accompanying diagram, AB and CD intersect at E. If m AEC = 4x 40 and m BED = x + 50, find the number of degrees in AEC. 17 Two angles are complementary. The measure of one angle is 15 more than twice the other. What is the measure of the smaller angle? 1) 25 2) 35 3) 55 4) In the accompanying diagram, line m is parallel to line p, line t is a transversal, m a = 3x + 12, and m b = 2x Find the value of x. 18 The accompanying diagram shows intersecting lines and m. Solve for the value of x. 19 In the accompanying figure, two lines intersect, m 3 = 6t + 30, and m 2 = 8t 60. Find the number of degrees in m In the accompanying diagram, parallel lines AB and CD are intersected by transversal EF at points X and Y, and m FYD = 123. Find m AXY. 4
5 23 Two parallel roads, Elm Street and Oak Street, are crossed by a third, Walnut Street, as shown in the accompanying diagram. Find the number of degrees in the acute angle formed by the intersection of Walnut Street and Elm Street. 25 The support beams on a bridge intersect in the pattern shown in the accompanying diagram. If AB and CD intersect at point E, m AED = 3x + 30, and m CEB = 7x 10, find the value of x. 24 In the accompanying diagram, CD EF, AB is a transversal, m DGH = 2x, and m FHB = 5x 51. Find the measure, in degrees, of BHE. 26 In the accompanying diagram, BY is a diameter of circle O, the measure of central angle ROY is (x + 60), and the measure of central angle ROB is (3x 20). Find the number of degrees in the measure of central angle ROY. 27 Two angles are complementary. One angle has a measure that is five times the measure of the other angle. What is the measure, in degrees, of the larger angle? 28 AB and CD intersect at E. If m AEC = 5x 20 and m BED = x + 50, find, in degrees, m CEB. 5
6 ID: A G.CO.C.9: Lines and Angles 3 Answer Section 1 ANS: 3 Vertical angles are complementary. REF: a 2 ANS: 1 and REF: a 3 ANS: 1 is congruent to are congruent alternate interior angles. because they are alternate interior angles. REF: a 4 ANS: 4 1 is supplementary to the angle of x degrees. REF: a 5 ANS: 2 REF: a 6 ANS: 4 Since 2 and 3 are congruent vertical angles, and 3 and 5 are supplementary same side interior angles, 2 and 5 are also supplementary. REF: a 7 ANS: 2 REF: spring9815a 8 ANS: 1 Since and the 30 angle are corresponding angles, REF: a 9 ANS: 1 Let x represent the acute angle that Jay Street forms with Main Street. Then 3x represents the obtuse angle that Jay Street forms with Brooks Road. Since the two angles are supplementary,. REF: a 10 ANS: 2 Same side exterior angles are supplementary. REF: a 11 ANS: 4 The sum of complementary angles is 90º. REF: a 1
7 ID: A 12 ANS: 2 The sum of complementary angles is 90º. REF: a 13 ANS: 4 The sum of supplementary angles is 180º. REF: a 14 ANS: 4 REF: a 15 ANS: 2 AEC and DEB are congruent vertical angles. REF: a 16 ANS: 1 The sum of complementary angles is 90º. REF: a 17 ANS: 1 The sum of complementary angles is 90º. REF: a 18 ANS: 8. Vertical angles are congruent. REF: a 19 ANS: and 3 are supplementary angles on one side of a stright line.. REF: a. 3 and 4 are congruent vertical angles. 2
8 ID: A 20 ANS: 80. Vertical angles are congruent. REF: a 21 ANS: 31. a and b are supplementary. REF: a 22 ANS: 57. Since FYD and CYX are congruent vertical angles, and CYX and AXY are supplementary same side interior angles, FYD and AXY are also supplementary. REF: a 23 ANS: 65. The acute angles are congruent alternate interior angles: REF: a 24 ANS: 146. DGH and FHB are congruent corresponding angles.. m FHB = 5(17) 51 = 34. Since FHB and BHE are supplementary angles, m BHE = 146 REF: a 25 ANS: 10. Vertical angles are congruent. REF: a 26 ANS: 95. ROB and ROY are supplementary angles on one side of a straight line.. REF: a. 3
9 ID: A 27 ANS: 75. The sum of supplementary angles is 180º.. REF: a 28 ANS: AEC and DEB are congruent vertical angles... BED and CEB are supplementary angles on one side of a straight line = REF: a 4
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