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.

$x=\dfrac{180^\circ}{6}$

$x=30^\circ$

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.