If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 4:5, then find the greater of the two angles.


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Answer:

100°

Step by Step Explanation:
  1. Let x be the first interior angle on the same side of a transversal intersecting two parallel lines.
  2. We know that the sum of two interior angles on the same side of a transversal intersecting two parallel lines is 180°.
    Thus, the second interior angle on the same side of a transversal intersecting two parallel lines = 180° - x

    The ratio of the two interior angles on the same side of a transversal intersecting two parallel lines =  
    x
    180° - x
     
  3. It is given that the ratio of the two interior angles on the same side of a transversal intersecting two parallel lines = 4:5
    Therefore,  
    x
    180° - x
      =  
    4
    5
     
    By cross multiplying, we get:
    5x = 4(180° - x)
    ⇒ 5x = 4 × 180° - 4x
    ⇒ 5x + 4x = 720°
    ⇒ 9x = 720°
    ⇒ x =  
    720
    9
     °
    ⇒ x = 80°
  4. The first angle = 80°
    The second angle = 180° - 80° = 100°
  5. Hence, the greater of the two angles is 100°.

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