Question

One of the angles is 20 degrees more than another angle. The third angle is 5 degrees less than the smaller of these. Find each angle.

Answer 1

There is no solution to this problem.

Step-by-step explanation:

Let's represent the three angles as x, x+20, and x-5.

According to the problem, x+20 = x-5+20.
Simplifying this equation, we get x+20 = x+15.

Solving for x, we subtract x from both sides and get 20 = 15, which is not true. Therefore, there is no solution to this problem.

Answer 2

One of the angles is 20 degrees more than another angle, the third angle is 5 degrees less than the smaller of these, the three angles are 55 degrees, 75 degrees, and 50 degrees.

Step-by-step explanation:

To find the angles, let's assign variables to each angle. Let's say the first angle is x degrees, the second angle is x + 20 degrees, and the third angle is x - 5 degrees.

We know that the sum of the angles of a triangle is 180 degrees, so we can write the equation:

x + (x + 20) + (x - 5) = 180

Combining like terms, we get:

3x + 15 = 180

Subtracting 15 from both sides, we have:

3x = 165

Dividing both sides by 3, we find that x = 55.

Therefore, the three angles are:

First angle: x = 55 degrees

Second angle: x + 20 = 55 + 20 = 75 degrees

Third angle: x - 5 = 55 - 5 = 50 degrees

So therefore the three angles are 55 degrees, 75 degrees, and 50 degrees.