Question

The angles of a triangle are in
the ratio 1: 2:3. then the
measure of each angle of the
triangle is ____degree​

Answer 1

Answer:

30 : 60 : 90

Step-by-step explanation:

Sum of angles in a triangle are supplementary,

1x + 2x + 3x = 180

6x = 180

x = 180 / 6

x = 30

1x = 30

2x = 60

3x = 90

30 : 60 : 90

Answer 2

Answer:

30°, 60° and 90°.

Step-by-step explanation:

Let the common multiple be 'x'.

So, now the angles are 1x, 2x and 3x.

We know that,

Sum of measure of three angles of triangle is 180°.

Therefore, 1x + 2x + 3x = 180°.

6x = 180°

x = $\frac{180}{6}$

x = 30°

So, the angles are-

1x = 1 × x = 1 × 30 = 30°

2x = 2 × x = 2 × 30 = 60°

3x = 3 × x = 3 × 30 = 90°

Verification:

Sum of measure of three angles of triangle is 180°,

1x + 2x + 3x = 180°

30° + 60° + 90° = 180°

180° = 180°

∵ LHS = RHS

The measure of each angle of the  triangle is 30°, 60° and 90°.