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Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT

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Angles

Based on the measurement, angles have been classified into different groups.

1. Complementary Angles

  • Two angles taken together are said to be complementary if the sum of measurement of the angles equal to 90o
  • If ∠ A + ∠ B = 90o then ∠A is complementary of ∠B and vice versa.

2. Supplementary Angles

  • Two angles are supplementary if the sum of their measure is 180o
  • If ∠ A + ∠ B = 180o then ∠A is supplementary of ∠B and vice – versa.

Question for Introduction: Angles & Lines
Try yourself:Two angles whose sum is equal to 180° are called:
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➢ Linear Pair

  • Two angles were drawn on the same point and have one arm common. The sum of these angles is 180o, then they are said to be linear pair of angles.
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT
  • ∠AOP and ∠POB are linear pair of angles.

➢ Adjacent Angles

  • Two angles are adjacent if and only if they have one common arm between them.
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT
  • In the above figure, ∠ABC and ∠BCD are adjacent angles, since they have BC as their common arm.

Properties of Lines

  • A line consists of infinite dots. A line is drawn by joining any two different points on a plane. Two different lines drawn can be either parallel or intersecting depending on their nature. 
  • If two lines intersect at a point, then they form two pairs of opposite angles (as shown in the figure), which are known as vertically opposite angles and have same measure. In the figure, ∠PRQ and ∠SRT are vertically opposite angles. 
  • Also, ∠QRS and ∠PRT are vertically opposite angles.
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT
  • Also, ∠x + ∠y = 180o and are Linear pair angles.
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT

 

➢ Perpendicular Lines

  • An angle that has a measure of 90o is a right angle. If two lines intersect at right angles, the lines are perpendicular.
    Example:
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT
    L1 and L2 above are perpendicular and denoted by L1 ⊥ L2.

➢ Parallel Lines

  • Two lines drawn on a plane are said to be parallel if they do not intersect each other. In the figure below lines, L1 and L2 are parallel and denoted by L1 || L2
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT

 

➢ Parallel lines and Transverse

  • If a common line intersects two parallel lines L1 and L2, then that common line is known as transverse.
    Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT
  • Pair of corresponding angles = (∠1 & ∠5) and (∠4 & ∠ 6)
  • Pair of internal alternate angles = (∠2 & ∠5)
  • Pair of exterior alternate angles = (∠3 & ∠6)
  • Vertically opposite angles = ∠3 & ∠4
  • For parallel lines intersected by the transversal, the pair of corresponding angles, interior alternate angles and exterior alternate angles are equal.
  • ∠1 = ∠5, ∠2 = ∠5, ∠3 = ∠6 and ∠3 = ∠4

Question for Introduction: Angles & Lines
Try yourself:If AB || CD, EF ⊥ CD and ∠GED = 135° as per the figure given below. The value of ∠AGE is:
Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT
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The document Introduction: Angles & Lines - Notes | Study Quantitative Aptitude (Quant) - CAT is a part of the CAT Course Quantitative Aptitude (Quant).
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