Question

The measures of angles of a triangle are in the ratio 1 : 2 : 3. Determine the measures of each angle of the triangle.

Answer 1

Let the ratio be x.

1st angle = 1x, 2nd angle = 2x, 3rd angle = 3x.

$\sf \: sum \: of \: angles \: of \: triangle = 180 \degree \\ \sf \: 1x + 2x + 3x = 180 \degree \\ \sf \: 6x = 180 \degree \\ \sf \: x = \frac{180}{6} \\ \sf \boxed{\boxed{ \sf{x = 30}}}$

Put x=30 in equations,

1st angle = 1x = 1×30 = 30°

2nd angle = 2x = 2×30 = 60°

3rd angle = 3x = 3×30 = 90°

Answer 2

Step-by-step explanation:

the sum of all angles Of a triangle = 180°

so first angle be 1x

second angle be 2x

third angle be 3x

$1x + 2x + 3x = 180 \\ 6x = 180 \\ x = 30$

first angle = 1x= 30

second angle = 2x= 60

third angle = 3x=90