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Angle Between Lines MCQs — Mathematics (page 2)

63 multiple-choice questions on Angle Between Lines from Mathematics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. Two lines with slopes m1 and m2 are parallel when:

  1. m1 m2 = -1
  2. m1 + m2 = 0
  3. m1 m2 = 1
  4. m1 = m2

Answer: D) m1 = m2

Explanation: Equal slopes give tantheta = 0, so theta = 0^circ. SLO M-09-B-10 · Knowledge

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27. The triangle has vertices A(1, 1), B(5, 2), C(2, 5). Find tan A.

  1. 158
  2. - 158
  3. 815
  4. 238

Answer: A) 158

Explanation: Slopes: mAB = 14, mAC = 4. Using tan A = mAC - mAB1 + mABmAC (with the sign that gives the interior angle) we get tan A = 158. SLO M-09-B-12 · Knowledge

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28. The line through the intersection of x - y - 5 = 0 and 3x - y - 11 = 0, parallel to the x-axis, is:

  1. y = 2
  2. y = 3
  3. x = 3
  4. y = -2

Answer: D) y = -2

Explanation: The lines meet at (3, -2); a line parallel to the x-axis through it is y = -2. SLO M-09-B-11 · Understanding

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29. When finding an interior angle of a triangle from slopes, a negative value of tan means the angle is:

  1. obtuse
  2. zero
  3. a right angle
  4. acute

Answer: A) obtuse

Explanation: tantheta < 0 for 90^circ < theta < 180^circ. SLO M-09-B-12 · Knowledge

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30. Find the acute angle between 2x - y = 0 and x + 2y - 5 = 0.

  1. 30^circ
  2. 45^circ
  3. 90^circ
  4. 60^circ

Answer: C) 90^circ

Explanation: Slopes m1 = 2, m2 = - 12. m1 m2 = -1, so theta = 90^circ. SLO M-09-B-10 · Knowledge

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31. If tantheta = 0 for the angle between two lines, the lines are:

  1. at 45^circ
  2. at 60^circ
  3. perpendicular
  4. parallel

Answer: D) parallel

Explanation: theta = 0^circ means the lines are parallel (or the same). SLO M-09-B-10 · Knowledge

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32. The angle between the x-axis and the line y = 3,x is:

  1. 30^circ
  2. 90^circ
  3. 45^circ
  4. 60^circ

Answer: D) 60^circ

Explanation: tantheta = 3, so theta = 60^circ. SLO M-09-B-10 · Knowledge

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33. Find the acute angle between lines with slopes 12 and 3.

  1. 45^circ
  2. 90^circ
  3. 30^circ
  4. 60^circ

Answer: A) 45^circ

Explanation: tantheta = m2 - m11 + m1 m2 = 52 52 = 1, so theta = 45^circ. SLO M-09-B-10 · Knowledge

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34. For the acute angle theta between lines with slopes 3 and - 12, tantheta =

  1. 72
  2. 75
  3. 7
  4. 17

Answer: C) 7

Explanation: tantheta = m2 - m11 + m1 m2 = - 72- 12 = 7. SLO M-09-B-10 · Knowledge

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35. Find the acute angle between lines with slopes 34 and - 17.

  1. 90^circ
  2. 60^circ
  3. 30^circ
  4. 45^circ

Answer: D) 45^circ

Explanation: tantheta = m2 - m11 + m1 m2 = - 2528 2528 = 1, so theta = 45^circ. SLO M-09-B-10 · Knowledge

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36. Find the acute angle between x - y = 0 and y - 5 = 0.

  1. 60^circ
  2. 45^circ
  3. 30^circ
  4. 90^circ

Answer: B) 45^circ

Explanation: Slopes m1 = 1, m2 = 0. tantheta = 1, so theta = 45^circ. SLO M-09-B-10 · Knowledge

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37. The triangle has vertices A(0, 0), B(6, 0), C(2, 4). Find tan A.

  1. -2
  2. 2
  3. 3
  4. 12

Answer: B) 2

Explanation: Slopes: mAB = 0, mAC = 2. Using tan A = mAC - mAB1 + mABmAC (with the sign that gives the interior angle) we get tan A = 2. SLO M-09-B-12 · Knowledge

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38. A triangle has sides with slopes 1, -1 and undefined (vertical). Which angles does it have?

  1. 90^circ, 60^circ, 30^circ
  2. 90^circ, 45^circ, 45^circ
  3. 135^circ, 22.5^circ, 22.5^circ
  4. 60^circ, 60^circ, 60^circ

Answer: B) 90^circ, 45^circ, 45^circ

Explanation: Slopes 1 and -1 are perpendicular; a vertical side makes 45^circ with each of them. SLO M-09-B-12 · Knowledge

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39. The triangle has vertices A(0, 0), B(4, 0), C(4, 3). Find tan A.

  1. - 34
  2. 43
  3. 74
  4. 34

Answer: D) 34

Explanation: Slopes: mAB = 0, mAC = 34. Using tan A = mAC - mAB1 + mABmAC (with the sign that gives the interior angle) we get tan A = 34. SLO M-09-B-12 · Knowledge

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40. Find the acute angle between 3x - y = 0 and x - 2y - 5 = 0.

  1. 30^circ
  2. 90^circ
  3. 60^circ
  4. 45^circ

Answer: D) 45^circ

Explanation: Slopes m1 = 3, m2 = 12. tantheta = 1, so theta = 45^circ. SLO M-09-B-10 · Knowledge

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41. Find the point of intersection of x + y - 5 = 0 and x + 3y - 13 = 0.

  1. (4, 1)
  2. (1, -4)
  3. (1, 4)
  4. (-1, 4)

Answer: C) (1, 4)

Explanation: Solve the two equations together: x = 1, y = 4. Check: both equations are satisfied by (1, 4). SLO M-09-B-11 · Understanding

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42. The lines x + y = 4, x - y = 2 and 2x + y = 7 are concurrent at:

  1. (3, 1)
  2. (2, 2)
  3. (1, 3)
  4. (4, 0)

Answer: A) (3, 1)

Explanation: The first two meet at (3, 1), and 2(3) + 1 = 7, so all three pass through (3, 1). SLO M-09-B-11 · Understanding

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43. The triangle has vertices A(-1, 0), B(3, 0), C(0, 3). Find tan A.

  1. 3
  2. 13
  3. -3
  4. 4

Answer: A) 3

Explanation: Slopes: mAB = 0, mAC = 3. Using tan A = mAC - mAB1 + mABmAC (with the sign that gives the interior angle) we get tan A = 3. SLO M-09-B-12 · Knowledge

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44. Find the point of intersection of x - y - 5 = 0 and 3x - y - 11 = 0.

  1. (3, -2)
  2. (3, 2)
  3. (-2, 3)
  4. (-3, -2)

Answer: A) (3, -2)

Explanation: Solve the two equations together: x = 3, y = -2. Check: both equations are satisfied by (3, -2). SLO M-09-B-11 · Understanding

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45. The triangle A(0, 0), B(4, 0), C(0, 4) has which angles?

  1. 60^circ, 60^circ, 60^circ
  2. 90^circ, 60^circ, 30^circ
  3. 120^circ, 30^circ, 30^circ
  4. 90^circ, 45^circ, 45^circ

Answer: D) 90^circ, 45^circ, 45^circ

Explanation: AB is horizontal and AC vertical, so angle A = 90^circ; BC has slope -1, giving 45^circ at B and C. SLO M-09-B-12 · Knowledge

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46. Find the line through the intersection of x + y - 5 = 0 and x + 3y - 13 = 0 that also passes through (0, 3).

  1. x + y + 3 = 0
  2. y - 3 = 0
  3. x - y - 3 = 0
  4. x - y + 3 = 0

Answer: D) x - y + 3 = 0

Explanation: The lines meet at (1, 4). The line through (1, 4) and (0, 3) is x - y + 3 = 0 (you can also use L1 + kL2 = 0 and find k from the point). SLO M-09-B-11 · Understanding

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47. The triangle has vertices A(0, 0), B(5, 0), C(1, 3). Find tan A.

  1. 4
  2. -3
  3. 13
  4. 3

Answer: D) 3

Explanation: Slopes: mAB = 0, mAC = 3. Using tan A = mAC - mAB1 + mABmAC (with the sign that gives the interior angle) we get tan A = 3. SLO M-09-B-12 · Knowledge

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48. Find the line through the intersection of 2x + y - 5 = 0 and x + 3y - 5 = 0 that also passes through (0, 0).

  1. 2x - y = 0
  2. x - 2y - 1 = 0
  3. x + 2y = 0
  4. x - 2y = 0

Answer: D) x - 2y = 0

Explanation: The lines meet at (2, 1). The line through (2, 1) and (0, 0) is x - 2y = 0 (you can also use L1 + kL2 = 0 and find k from the point). SLO M-09-B-11 · Understanding

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49. For the acute angle theta between lines with slopes 2 and - 13, tantheta =

  1. 73
  2. 7
  3. 75
  4. 17

Answer: B) 7

Explanation: tantheta = m2 - m11 + m1 m2 = - 73 13 = 7. SLO M-09-B-10 · Knowledge

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50. The triangle has vertices A(2, 1), B(6, 1), C(4, 5). Find tan A.

  1. 2
  2. -2
  3. 3
  4. 12

Answer: A) 2

Explanation: Slopes: mAB = 0, mAC = 2. Using tan A = mAC - mAB1 + mABmAC (with the sign that gives the interior angle) we get tan A = 2. SLO M-09-B-12 · Knowledge

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