In a quadrilateral ABCD, the angles A, B, C and D are in ratio 1:2:3:4. Find the measure of each angle of the quadrilateral.


  1. Home
  2. Math
  3. All Questions
Answer:

∠A = 36°, ∠B = 72°, ∠C = 108°, ∠D = 144°

Step by Step Explanation:
  1. Let's assume x is the common factor of the angles of the quadrilateral.
    According to the question, the angles A, B, C and D are in ratio 1:2:3:4.
    Therefore,
    ∠A = 1x,
    ∠B = 2x,
    ∠C = 3x and
    ∠D = 4x.
  2. We know that the sum of all interior angles of a quadrilateral is equal to 360°.
    Therefore, ∠A + ∠B + ∠C + ∠D = 360°
    ⇒ 1x + 2x + 3x + 4x = 360°
    ⇒ 10x = 360
    ⇒ x =  
    360
    10
     
    ⇒ x = 36
  3. Hence, ∠A = 1x = 1 × 36 = 36°,
    ∠B = 2x = 2 × 36 = 72°,
    ∠C = 3x = 3 ×36 = 108° and
    ∠D = 4x = 4 × 36 = 144°.

You can reuse this answer
Creative Commons License