Question

The ratio of the measures of the three angles in a triangle is 10:3:7. Find the measure of the largest angle

Answer 1

Answer:

The ratio of the measures of the three angles in a triangle is 10:3:7. Find the measure of the largest angle

Answer 2

Given:

The ratio of the measures of the three angles in a triangle is 10:3:7.

To find:

The measure of the largest angle.

Solution:

The measure of the largest angle is 90°.

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 10:3:7

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

So,

the three angles are 10x, 3x and 7x.

Hence,

$10x + 3x + 7x = 180°$

$20x = 180$

$x = 9$

So,

the three angles are

10x = 10(9) = 90°

3x = 3(9) = 27°

7x = 7(9) = 63°

So, the largest angle is 90°.