The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle Pick one
A) 45o	B) 45o	C) 66o	D) 72 degree	E) None of these
Solution:   Let a and b be the two angles in the question, with a &gt; b. We are given that the difference between the angles is 24o.   =&gt; a – b = 24.   Since the average of the two angles is 54o, we have (a+b)/2 =54.   Solving for b in the first equation yields b=a–24, and substituting this into the second equation yields,   [{a+(a−24)}/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   180o, 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 equ   Answer: Option 72 degree
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The difference between two angles of a triangle is 24o. The average of the same two angles is 54o. Which one of the following is the value of the greatest angle of the triangle