Question

The angles of a triangle are in the ratio 11:15:10
What is the size of the largest angle?

Answer 1

Let the three angles of the triangle be 11x, 15x, and 10x. The sum of the angles of a triangle is 180 degrees, so:

11x + 15x + 10x = 180

Simplifying the left side, we get:

36x = 180

Dividing both sides by 36, we get:

x = 5

So the three angles are:

11x = 55 degrees
15x = 75 degrees
10x = 50 degrees

Therefore, the largest angle is 75 degrees.

Answer 2

75°

Explanation:

Let their common multiple be 'x'

Thus, the 3 angles are 11x, 15x, 10x

We know, the sum of all angles of a triangle is 180°

∴ 11x + 15x + 10x = 180°

∴ 36x = 180°

∴ x = 5

The largest angle, 15x = 15 × 5 = 75°