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?

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? Correct Answer 72°

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 = 24Since the average of the two angles is 54°, we have $$\frac{{{\text{a}} + {\text{b}}}}{2}$$  = 54Solving 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 × 22a − 24 = 1082a = 108 + 242a = 132a = 66Also,b = a − 24 = 66 − 24 = 42Now, 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.