Given:

✰ The MEASURE of three angles of a triangle are in the ratio 5:3:1.

To find:

✠ The three angles of the triangle.

Solution:

Triangle:

The three-sided closed figure is called triangle.

Let's understand the concept first! First we will assume that the measure of three angles of a triangle are 5x, 3x and x respectively. Then, we will use of interior angle of a triangle. It states that the sum of the interior angle of a triangle is ALWAYS equal to 180°. Thus, forming an equation and doing the required CALCULATIONS, we will find out the VALUE of x. After that we will substitute the value of x in the respective measure of angles which we have assumed to GET the final angles of a triangle.

Let's find out...!

Let the angles of the triangle be 5x, 3x and x respectively.

Sum of interior angles of a triangle is always 180°

➤ 5x + 3x + x = 180

➤ 8x + x = 180

➤ 9x = 180

➤ x = 180/9

➤ x = 20°

Now,

➛ First angle = 5x

➛ First angle = 5 × 20

➛ First angle = 100°

➛ Second angle = 3x

➛ Second angle = 3 × 20

➛ Second angle = 60

➛ Third angle = x

➛ Third angle = 20°

∴ The measure three angles of the triangle are 100°, 60° and 20° respectively.

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