Question

the ratio of the three angles in a triangle 2:9:4. what are the measures of the angles

Answer 1

Let the three angles be 2x,9x & 4x

By the problem,2x+9x+4x=180

15x=180

x=180/15

x=12

there fore the angles are

2x= 2*12=24°

9x=108°

4x=48°

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Answer 2

Given:

The ratio of the measures of the three angles in a triangle is 2:9:4.

To find:

The measure of all angles.

Solution:

The measure of all angles is 24°, 108° and 48°.

To find the answer, we will follow the following steps.

As we know that in a triangle having angles angle l, angle m and angle n, the sum of all angles is equal to 180°.

This means,

angle l + angle m + angle n = 180°

Now, as given,

The ratio of three angles in a triangle is 2:9:4.

Let the common ratio between all angles of a triangle be x.

So,

the three angles are 2x, 9x and 4x.

Hence,

$2x + 9x + 4x = 180°$

$15x = 180$

$x = 12$

So,

the three angles are

2x = 2(12) = 24°

9x = 9(12) = 108°

4x = 4(12) = 48°

So, the three angles of the given triangle are 24°, 108° and 48°.