Question

The angles of a traingle are in the ratio of 6:5:9 the angles are​

Answer 1

Answer:

54,45 and 81

Step-by-step explanation:

Let the angles be 6x,5x and 9x

we know that 6x + 5x + 9x = 180 --- angle sum property of triangle

20x = 180

x = 180/20

x= 9

hence 3 angles are

6x = 6×9=54

5x= 5×9=45

9x= 9×9=81

Answer 2

Answer :

Here, we are given the ratio of the three angles of the triangle and we need to calculate the measure of all the three angles. For that firstly we will assume the three angles of the triangle as any variable, according to the ratio given. And then by using the formula of sum of interior angles of polygon we will get our required answer.

Formula of sum of interior angles of polygon :

$\bf{Sum ~ of ~interior ~angles ~of~polygon~=(2n - 4) \times 90^{\circ}}$

where,

• n denotes the number of sides

Solution :

Given :

• Ratio of the three angles of triangle = 6 : 5 : 9

To find :

• The measure of three angles of triangle

Required Solution :

Let the three angles of triangle be 6x, 5x and 9x.

• First angle = 6x
• Second angle = 5x
• Third angle = 9x

⇒ Triangle has 3 angles, 3 sides.

⇒ Number of sides (n) = 3

⇒ Sum of interior angles of triangle = (2n - 4) × 90°

⇒ 6x + 5x + 9x = (2(3) - 4) × 90°

⇒ 20x = (6 - 4) × 90°

⇒ 20x = (2) × 90°

⇒ 20x = 180°

⇒ x = 180°/20

⇒ x = 18°/2

⇒ x = 9°

Substituting the value of ' x ' in the angles :

FIRST ANGLE :

⇒ First angle = 6x

⇒ First angle = 6(9°)

⇒ First angle = 54°

SECOND ANGLE :

⇒ Second angle = 5x

⇒ Second angle = 5(9°)

⇒ Second angle = 45°

THIRD ANGLE :

⇒ Third angle = 9x

⇒ Third angle = 9(9°)

⇒ Third angle = 81°

Therefore, the three angles of triangle are 54°, 45° and 81°