The two angles of the triangle are 5: 9, and the third angle is 10 degrees

The two angles of the triangle are 5: 9, and the third angle is 10 degrees less than the smaller of these angles. Find the smallest angle of the triangle.

1. Let’s denote one part by x.

2. The two corners of the triangle will be equal:

5x and 9x.

3. Let’s define the degree measure of the third angle:

(5x – 10).

4. Since the sum of the angles of the triangle is 1800, compose and solve the equation:

5x + 9x + (5x – 10) = 180;

5x + 9x + 5x – 10 = 180;

19x – 10 = 180;

19x = 180 + 10;

19x = 190;

x = 190: 19;

x = 10.

5. One part is equal to x = 10.

6. What is the smaller angle of the triangle?

5 * 10 = 50.

7. What is the second angle of the triangle?

9 * 10 = 90.

8. What is the degree measure of the third angle of the triangle?

50 – 10 = 40.

Answer: the angles of the triangle are 50, 90, 40.