The difference between two angles of a triangle is 24 The…

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The difference between two angles of a triangle is 24°. The average of the same two angles is 54°. Which one of the following is the value of the greatest angle of the triangle?

  1. A. 45°
  2. B. 60°
  3. C. 66°
  4. D. 72°

Answer: Option D

Here is complete explanation of The difference between two angles of a triangle is 24 The….

Solution(By ExamCraze Team)

Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24°. ⇒ a – b = 24 Since the average of the two angles is 54°, we have $$frac{{{text{a}} + {text{b}}}}{2}$$  = 54 Solving for b in the first equation yields b = a – 24, and substituting this into the second equation yields, $$ {frac{{left{ {{text{a}} + left( {{text{a}} - 24} right)} right}}}{2}} = 54$$ 2a − 24 = 54 × 2 2a − 24 = 108 2a = 108 + 24 2a = 132 a = 66 Also, b = a − 24 = 66 − 24 = 42 Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is 180°, a + b + c = 180° Putting the previous results into the equation yields 66 + 42 + c = 180° Solving for c yields c = 72° Hence, the greatest of the three angles a, b and c is c, which equal.

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