If lines XY and MN intersect as shown below and a:b = 1:2, find c.


Answer:

120°

Step by Step Explanation:
  1. As XY is a straight line, and the sum of the angles on a straight line is equal to 180°.
    We have, a + b + 90° = 180°
    ⇒ a + b = 90°.
  2. We may notice that the angles MOY and XON are vertically opposite angles.
    So, a + 90° = c (vertically opposite angles are equal).
  3. We are given a:b = 1:2, or  
    a
    b
      =  
    1
    2
     .
    Cross multiplying the fractions, we get,
    2a = 1b.
  4. We put b = 2a in a + b = 90° and get,
    a + 2a = 90°, or 3a = 90°. Dividing each side by 3, we get,
    a =  
    90°
    3
     , or 30°.
  5. Now, since b = 2a.
    We can say that b = 2 × 30°, or b = 60°.
  6. From step 2, we have,
    c = a + 90°, or c = 30° + 90°,
    or c = 120°.

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