Question

In a triangle ABC, if 2∠A = 3∠B = 6∠C, then the measure of ∠A in degree is?​

Answer 1

in triangle ABC

∠A+ ∠B + ∠C = 180

so,

let ∠A = x & ∠B = y then

∠C = 180-(x+y)

2∠A = 3∠B = 6∠C

2x = 3y = 6(180-(x+y))

2x = 3y = (1080 - 6x - 6y)------>1

from (1)

3y = 1080 - 6x -6y

y = 360 - 2x - 2y

3y = 360 - 2x ------>2

from (1)

2x = 3y

from (2)

3y = 360 - 2x

2x = 360 - 2x

4x = 360

x = 360 / 4

x = 90

2x = 3y

2×90 = 3y

3y = 180

y = 60

∠C = 180-(x+y)

= 180 -(90+60)

= 180 - 150

∠C = 30

∠A = 90 & ∠B = 60 then ∠C = 30

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