Math Quiz 2 1 - 2 4 Review Answer Key

Quiz Review 2.1-2.4 Name: KEY Vocabulary Choose from the words in the bank below to fill in the blanks with the correct vocabulary word. linear pair bisect segment bisector adjacent midpoint 90° angle bisector 180° complementary vertical angles The midpoint of a segment is the point on the segment that divides it into two congruent segments. A segment bisector is a segment, ray, line or plane that intersects a segment at its midpoint. To bisect a segment means to divide the segment into two congruent segments. Two angles are complementary if the sum of their measures is 90°.   Two angles are supplementary if the sum of their measures is 180°. If two angles share a common vertex and side, but have no common interior points, then the two angles are adjacent angles.   M is the midpoint of the segment. Find the segment lengths. Find TM and MR. Line l bisects the segment. Find the segment lengths. 11. Find AN and AB. [Image of a line segment AB with midpoint N and lengths AN and NB] AN = 9.2 AB = 18.4 12. Find FG and EG. [Image of a line segment EG with midpoint F and lengths FG and EG] FG = 17 EG = 34 Line l bisects the segment. Find the value of x. 13. [Image of a line segment JK with midpoint L and lengths JL = 3x+6 and LK = 15] 3x + 6 = 15 3x = 9 x = 3 14. [Image of a line segment VW with midpoint X and lengths VX = 28 and WX = 5x+3] 5x + 3 = 28 5x = 25 x = 5 Find the coordinates of the midpoint of AB. 15. A(-2, 3), B(4, -1) ((-2+4)/2, (3+(-1))/2) = (1, 1) 16. A(-6, 1), B(-2, 7) ((-6+(-2))/2, (1+7)/2) = (-4, 4) 17. A(4, 0), B(6, -8) ((4+6)/2, (0+(-8))/2) = (5, -4) GE bisects ∠FGH. Find the angle measure. 18. Find m∠EGH. [Image of an angle FGH with bisector GE and angle EGH = 23 degrees] m∠EGH = 23° 19. Find m∠FGE. [Image of an angle FGH with bisector GE and angle FGE = 70 degrees] m∠FGE = 70° 20. Find m∠EGF. [Image of an angle FGH with bisector GE and angle EGF = 45 degrees] m∠EGF = 45° BA bisects ∠DBC. Find m∠CBA and m∠DBC. 21. [Image of an angle DBC with bisector BA and angle DBA = 35 degrees] m∠CBA = 35° m∠DBC = 70° 22. [Image of an angle DBC with bisector BA and angle DBA = 75 degrees] m∠CBA = 75° m∠DBC = 150° 23. [Image of an angle DBC with bisector BA and angle DBA = 45 degrees] m∠CBA = 45° m∠DBC = 90° JK bisects ∠GJH. Find the value of x. (Bisects means cuts in ½) 24. [Image of an angle GJH with bisector JK and angles 4D and x+16] Equation: 4D = x + 16 x = 30 25. [Image of an angle GJH with bisector JK and angles 4x and 80] Equation: 4x = 80 x = 20 26. [Image of an angle GJH with bisector JK and angles 6x and 18] Equation: 6x = 18 x = 3 Find the measure of the complement of the angle. (Complements add up to 90°) 27. m∠Y = 35° 35° + x = 90° x = 55° 28. m∠A = 89° 89° + x = 90° x = 1° 29. m∠B = 17° 17° + x = 90° x = 73° Find the measure of the supplement of the angle. (Supplements add up to 180°) 30. m∠A = 54° 54° + x = 180° x = 126° 31. m∠B = 175° 175° + x = 180° x = 5° 32. m∠C = 115° 115° + x = 180° x = 65° ∠PQS and ∠SQR are complementary angles. Find the value of the variable. 33. [Image of two complementary angles PQS and SQR with angles 4x and 5x] These angles add up to 90°. Equation: 4x + 5x = 90 9x = 90 x = 10 34. [Image of two complementary angles PQS and SQR with angles 4x+10 and 4x] These angles add up to 90°. Equation: 4x + 4x + 10 = 90 8x + 10 = 90 8x = 80 x = 10 35. [Image of two complementary angles PQS and SQR with angles 3x+8 and x+2] These angles add up to 90°. Equation: 3x + 8 + x + 2 = 90 4x + 10 = 90 4x = 80 x = 20 Use the figure at the right to complete the statement. 36. ∠1 and ∠2 are a linear pair, and so are ∠1 and ∠4 37. ∠2 and ∠3 are vertical angles. 38. If m∠3 = 150°, then m∠2 = 30° 39. m∠4 = ∠2 Find the measure of the numbered angle. 40. [Image of two intersecting lines forming vertical angles] These angles add up to 180°. Equation: 151° + m∠2 = 180° m∠2 = 29° 41. [Image of two intersecting lines forming vertical angles] These angles are vertical. Equation: m∠4 = 154° 42. [Image of two intersecting lines forming a linear pair] These angles add up to a linear pair. Equation: 91° + m∠5 = 180° m∠5 = 89° Find m∠1, m∠2, and m∠3. 43. [Image of two intersecting lines] m∠1: 145° m∠2: 35° m∠3: 145° 44. [Image of two intersecting lines] m∠1: 90° m∠2: 90° m∠3: 90° 45. [Image of two intersecting lines] m∠1: 52° m∠2: 128° m∠3: 52° Find the value of the variable. Then use substitution to find m∠PQR. 46. [Image of a triangle PQR with angles 4x-11, x+8, and 31 degrees] Equation: 4x-11 + x+8 = 31 5x - 3 = 31 5x = 34 x = 6.8 m∠PQR = 4(6.8) - 11 = 21.2° 47. [Image of a triangle PQR with angles 104, 3y+2, and 5x] Equation: 104 + 3y+2 = 180 3y = 74 y = 24.67 m∠PQR = 3(24.67) + 2 = 76.01° 48. [Image of a triangle PQR with angles 3x+12, 5x, and 6] Equation: 3x+12 + 5x = 180 8x + 12 = 180 8x = 168 x = 21 m∠PQR = 3(21) + 12 = 75° Find the value of the variable. 49. [Image of two intersecting lines with angles 4x-1, x+81, and 5x] Equation: 4x-1 + x+81 = 180 5x + 80 = 180 5x = 100 x = 20 50. [Image of two intersecting lines with angles x^2-4x, 148, and 4x] Equation: x²-4x + 148 = 180 x²-4x-32 = 0 (x-8)(x+4) = 0 x = 8, -4 (discard -4) m∠PQR = 4(8) + 5(8) = 72° 51. [Image of two intersecting lines with angles 4x, 5x, and 6] Equation: 4x + 5x = 180 9x = 180 x = 20 m∠PQR = 3(20) + 12 = 72°