Question

the angles of a triangle are in the ratio 1:2:3. find the measure of the angle of that tringle

Answer 1

HEY THERE!!

Question:

The angles of a triangle are in the ratio 1:2:3. find the measure of the angle of that triangle.

Method of Solution:

Let to Required Angle be 'X'

Angles of Triangle  are in the form of Ratio with x = x:2x:3x

Note: Sum of all Angles of Triangle = 180°

Thus, Sum of angles of ∆ =180°

=> x+2x+3x = 180°

=> 6x = 180°

•°• x= 180°/6

=> 30°

Hence, Value of x = 30°

Now, According to the Question:

find the measure of the angle of that tringle:

Measurements of First Angle => x = 30°

Measurements of Second Angle => 2x = 60°

Measurements of third Angle => 3x = 90°

Verification of All angles must be 180°

=> First Angle + Second Angle + Third Angle

=> 30° + 60° + 90°

=> 180°

Hence, It's Proved!!

Answer 2

Given: The angles of a triangle are in the ratio 1:2:3.  

To find: The measure of the angle of that tringle.

Solution:

Let one of the angles of the triangle be x. Hence, the other two angles can be written as 2x and 3x. These three angles would sum up to give a sum of 180 because the sum of the angles of a triangle is equal to 180. This can be stated by the following equation.

$x+2x+3x = 180$

$6x = 180$

$x = 30$

The measure of the first angle is 30°. Thus, the measure of the other two angles can be calculated as follows.

$2x = 2*30$

    $= 60$

$3x =3 *30$

    $= 90$

Therefore, the measure of the angles of that triangle is 30°, 60° and 90°.