Question

Th second angle of a triangle is three times as large as the first. The measure of the third angle is 40 degrees greater than that of the first angle. How large are the three angles?

Answer 1

The three angles of the triangle are 28 degrees, 84 degrees, and 68 degrees.

Step-by-step explanation:

Let x be the measure of the first angle.

According to the first condition, the second angle is three times as large as the first angle, so the second angle is 3x.

The third angle is 40 degrees greater than the first angle, so it is x + 40.

The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:

1. x + 3x + (x + 40) = 180

Simplifying the equation:

1. 5x + 40 = 180
2. 5x = 140
3. x = 28

So, the first angle is 28 degrees.

The second angle is three times as large, so it is 3x = 3(28) = 84 degrees.

The third angle is x + 40 = 28 + 40 = 68 degrees.

Therefore, the three angles are 28 degrees, 84 degrees, and 68 degrees.

Learn more about Triangle angles