Question

In a triangle abc, if 2angleA=3 angle B=6 angle C find the measures of each angles

Answer 1

2angleA=3angleB=6angleC
=angleA+angleB+angleC=180(angle sum property) ----eq1

let x=2angleA=3angleB=6angleC
x=2angleA. x/2=angleA. ----eq2
x=3angleB. x/3=angleB. ----eq3
x=6angleC. x/6=angleC. ----eq4

substituting eq2,3,4 in eq1

x/2+x/3+x/6=180
Lcm=6
3x+2x+x/6=180
6x=180×6
6x=1080
x=180------eq 5

substituting eq 5 in eq 2,3,4

angleA=x/2=90
angleB=x/3=60
angleC=x/6=30

hope this helps

Answer 2

2angleA=3angleB=6angleC

=angleA+angleB+angleC=180(angle sum property) ----eq1

let x=2angleA=3angleB=6angleC

x=2angleA. x/2=angleA. ----eq2

x=3angleB. x/3=angleB. ----eq3

x=6angleC. x/6=angleC. ----eq4

substituting eq2,3,4 in eq1

x/2+x/3+x/6=180

Lcm=6

3x+2x+x/6=180

6x=180×6

6x=1080

x=180------eq 5

substituting eq 5 in eq 2,3,4

angleA=x/2=90

angleB=x/3=60

angleC=x/6=30

hope this helps