Question

if one angle is the average of other two angles and difference between the greatest and least angles is 60 then formed triangle is? options 1) isosceles 2) an equilateral triangle 3) a right angle triangle. 4) none of these​

Answer 1

Answer:

Right angle triangle

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Answer 2

Answer:

3 - right angle triangle

Step-by-step explanation:

sum of three angles of a triangle is 180

a + b + c = 180

a = (b + c)/2

$\frac{b + c}{2} + b + c = 180 \\ \frac{b + c + 2b + 2c}{2} = 180 \\ 3b + 3c = 180 \times 2 = 360 \\ 3(b + c) = 360 \\ b + c = 120 \: \: \: \: equ \: (1) \\ a = \frac{b + c}{2} = \frac{120}{2} = 60 \\ given \: that \: greatest \: angle \: is \: 60 \: more \: than \: smallest \: angle \\ b - c = 60 \: \: equ \: (2) \\ \\ equ \: (1) - (2) \\ 2b = 180 \\ b = \frac{180}{2} = 90 \\ b - c = 60 \\ 90 - c = 60 \\ c = 30 \\ a = 60 \: \: \: b = 90 \: \: \: c = 30$