24.The measure of three angles of a triangle are in the ratio 5:3:1. Find the three angles
of the triangle?
ples
Answers
Let the angles of the triangle be 5y, 3y and y.
∴ y+3y+5y = 180
o
⇒ 9y = 180
o
⇒ y = 20
o
⇒ 3y = 3×20
o
= 60
o
⇒ 5y = 5×20
o
= 100
o
Therefore, angles of triangle are 20
o
, 60
o
and 100
o
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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