Question

get?
17. If the angles of a triangle are in the ratio 4:5:9, find the measures of the angles of the
triangle and name the type of triangle.
amono A. B. and C in the ratio 2: 7:4.​

Answer 1

Answer :

›»› The three angles of a triangle are 40°, 50°, and 90°, and it is a scalene triangle.

Step-by-step explanation :

Given :

• The angles of a triangle are in the ratio 4:5:9.

To Find :

• The measure of all angles of a triangle.
• Name the type of triangle.

Knowledge required :

The sum of all three angles of a triangle is 180°.

This statement is known as angle sum property of triangle.

Solution :

Let us assume that, the three angles of a triangle is 4x, 5x, 9x respectively.

As we know that

The sum of all three angles of a triangle is 180°.

→ 4x + 5x + 9x = 180

→ 9x + 9x = 180

→ 18x = 180

→ x = 180/18

→ x = 10

Therefore,

The three angles of a triangle will be,

• 4x = 4 × 10 = 40.
• 5x = 5 × 10 = 50.
• 9x = 9 × 10 = 90.

We know that, if all angles of a triangle are different angles then the triangle is scalene triangle.

Here all angles are different so this is a scalene triangle.

Hence, the three angles of a triangle are 40°, 50°, and 90°, and it is a scalene triangle.