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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?

A. 45°

B. 60°

C. 66°

D. 72°

Answer: Option D

Solution(By Examveda 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.

This Question Belongs to Arithmetic Ability >> Average

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Comments ( 1 )

  1. Md Maruf
    Md Maruf :
    3 years ago

    shortcut
    a-b = 24
    a+b = 108
    2a = 132 or a = 66 then b = 42
    we know,
    a+b+c = 180 then c = 72

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