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Question

The largest angle of a triangle is twice the sum of the other two. The smallest is one-fifth of the largest. Determine all the angles in degrees.

A
120o,36o,24o
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B
15o,85o,800
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C
85o,15o,800
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D
20o,136o,240
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Solution

The correct option is A 120o,36o,24o
Let A is the largest and C is the smallest angle.
According to question:
A=2(B+C) and C=15A
B+C=12A ....(i) and C=15A ...(ii)
since,
A+B+C=180o ...(iii)
A+12A=180o (from (i))
12(3A)=180o
3A=360oA=120o
So,
C=15(120o)=24o (using (ii))
On substituting the value of A and C in (iii). we get,
120o+B+24o=180o
B=36o
A=120o,B=36o,C=24o

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