Question

In a triangle ABC , if 2∠A=3∠B=6∠C, then find the measure of ∠B.​

Answer 1

Question is In a triangle ABC , if 2∠A=3∠B=6∠C, then find the measure of ∠B.

ANSWER

Let all the angles be x.

∠A=

2

x

,∠B=

3

x

,∠C=

6

x

So,

2

x

+

3

x

+

6

x

=180° [sum of all the angles of triangle is 180°]

12

6x+4x+2x

=180°

12

12x

=180°

x=180°

∠A=

2

x

=

2

180°

=90°

∠B=

2

x

=

3

180°

=60°

∠C=

6

x

=

6

180°

=30°

Answer 2

Let all the angles be x.

∠A=2x,∠B=3x,∠C=6x

So, 2x+3x+6x=180°    [sum of all the angles of triangle is 180°]

126x+4x+2x=180°

1212x=180°

x=180°

∠A=2x=2180°=90°

∠B=2x=3180°=60°

∠C=6x=6180°=30°