Question

In ∆ABC, 2<A = 3<B = 6<C, find the smallest angle of the triangle.​

Answer 1

Answer:  30°

Step-by-step explanation:

2A = 3B = 6C

2A = 6C  =>  A = 3C  ..... (i)

3B = 6C  =>  B = 2C ..... (ii)

Since A + B + C = 180°     (Angle sum property of triangle)

=>  3C + 2C + C = 180°    (from (i) and (ii))

=>  6C = 180°

=>  C = 30°

A = 3C = 3 x 30 = 90°

B = 2C = 2 x 30 = 60°

C = C = 30°

Since 30° < 60° < 90°,

Smallest angle possible is 30°

Hope it helps...

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