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

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 90^o. 
• If ∠ A + ∠ B = 90^o then ∠A is complementary of ∠B and vice versa.

2. Supplementary Angles

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

➢ Linear Pair

• Two angles were drawn on the same point and have one arm common. The sum of these angles is 180^o, then they are said to be linear pair of angles.
  
• ∠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.
  
• 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.
  
• Also, ∠x + ∠y = 180^o and are Linear pair angles.
  

➢ Perpendicular Lines

• An angle that has a measure of 90^o is a right angle. If two lines intersect at right angles, the lines are perpendicular.
  Example:
  
  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
  

➢ Parallel lines and Transverse

• If a common line intersects two parallel lines L1 and L2, then that common line is known as transverse.
  
• 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:

• A.

  120°
• B.

  135°
• C.

  90°
• D.

  45°

Explanation

Since AB || CD and GE is transversal.
Given, ∠GED = 135°
Hence, ∠GED = ∠AGE = 135° (Alternate interior angles)

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