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,24oLet ∠A is the largest and ∠C is the smallest angle.According to question:∠A=2(∠B+∠C) and ∠C=15∠A∴∠B+∠C=12∠A ....(i) and ∠C=15∠A ...(ii)since,∠A+∠B+∠C=180o ...(iii)∴∠A+12∠A=180o (from (i))∴12(3∠A)=180o∴3∠A=360o⇒∠A=120oSo,∠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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