Question

The ratio of the measures of the angles of a triangle is 1:2:3 find the measures of each angle​

Answer 1

Given:

The ratio of the measures of the angles of a triangle is 1:2:3.

To find:

The measures of each angle​.

Solution:

Let the measure of angles be x, 2x and 3x respectively.

We know that, sum of all the interior angles of a triangle is 180 degrees by the angle sum property.

Using angle sum property, we get

`x+2x+3x=180^\circ`

`6x=180^\circ`

Divide both sides by 6.

`x=(180^\circ)/(6)`

`x=30^\circ`

Now,

First angle:
`30^\circ`

Second angle:
`2(30^\circ)=60^\circ`

Third angle:
`3(30^\circ)=90^\circ`

Therefore, the measure of all the angles are 30°, 60° and 90° respectively.