Question

in triangle abc,if 2angleA=3angleB=6angleC,determine the measures of each angles.

Answer 1

hey, mate here is ur solution
$we \: know \: that \\ \alpha + \beta + \gamma = 180 \: equation1\\ 2 \alpha = 3 \beta = 6 \gamma \\ \beta = 2 \gamma \: equation \: 2 \\ and \: \\ \alpha = 3 \gamma \: equation \: 3\\ now \: put \: value \: of \: \alpha \: and \ \: beta \: in \: equation1 \\ 6 \gamma = 180 \\ (\gamma = 30 )\\ put \: value \: of \: \gamma \: in \: equation \: 2 \: and \: in \: 3\\ (\beta = 60 )\\ (\alpha = 90)$

Answer 2

Let angle A = x

Find Angle B in term of x

3 angle B = 2x

angle B = 2/3 x

Find Angle C in term of x

6 Angle C = 2x

Angle C = 1/3 x

Solve x:

Sum of all then angles in a triangle is 180°

x + 2/3 x + 1/3 x = 180

2x = 180

x = 90

Find the angles:

Angle A = x = 90°

Angle B = 2/3 x = 2/3 (90) = 60°

Angle C = 1/3 x = 1/3 (90) = 30°

Answer: Angle A is 90°, Angle B is 60° and Angle C is 30°