Question

In a triangle ABC , if 2 angle A =3 angle B =6 angle C ,calculate the measure of angle B

Answer 1

heya..m using /, to denote angle.
2,a=3,b=6,c=x

2,a=x
,a=x/2

3,b=x
,b=x/3

6,c=x
,c=x/6

x/2+x/3+x/6=180
3x+2x+x/6=180
6x/6=180
x=180×6/6
x=180
,b=/3=180/3=60°

Answer 2

Given,
2 ∠A = 3 ∠B = 6 ∠C

∠A = 3/2 ∠B

∠C = 3/6 ∠B= 1/2 ∠B

By Angle - Sum property ;

∠A + ∠B + ∠C =180

3/2 ∠B + ∠B + 1/2 ∠B =180

2 ∠B + ∠B =180

3 ∠B = 180

∠B =60°.