Question

The largest angle of a triangle is three times the middle angle. The smallest angle measures 15° less than the middle angle. Find the measure of each angle.

Part: 0/3
Part 1 of 3

Answer 1

The measure of the angles in the triangle is 39°, 24°, and 117°.

Step-by-step explanation:

Let x be the measure of the middle angle.

The largest angle is three times the middle angle, so it is 3x.

The smallest angle is 15° less than the middle angle, so it is x - 15.

The sum of the angles in a triangle is always 180°. Therefore, we can write the equation:

x + 3x + (x - 15) = 180

Combining like terms, we have:

5x - 15 = 180

Adding 15 to both sides, we get:

5x = 195

Dividing both sides by 5, we obtain:

x = 39

The middle angle is 39°, the smallest angle is 39° - 15° = 24°, and the largest angle is 3(39°) = 117°.

Learn more about Angles in a triangle