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.Join The Discussion
Comments ( 1 )
Related Questions on Average
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
D. 120 km/hr
shortcut
a-b = 24
a+b = 108
2a = 132 or a = 66 then b = 42
we know,
a+b+c = 180 then c = 72