Find the angles of a triangle if one of these angles is half the second angle and 80 degrees less than the third

Let the base angle be equal to the variable a.

Then, in accordance with the conditions, the second angle can be represented using 2a.

Therefore, it will be possible to write the third angle through a + 80.

Since we know from the condition of the problem that these are the angles of a triangle, we have the opportunity to write down the equation and find out what each will equal:

a + 2a + a + 80 = 180;

4a = 100;

a = 25;

2 * 25 = 50;

25 + 80 = 105.

Answer: The first angle will be 25 °, the second will be 50 °, and the third will be 105 °.