The measures of the angles of triangle are in the ratio 2: 5: 5. what are the measures of the angles?

30°, 75°, and 75°

Step-by-step explanation:

You need to know that triangle angle measures ALWAYS add up to 180°.  

You need to know that ratios tell you how many total parts there are.

Here, the angles are 2 parts, to 5 parts, to 5 parts.  That means there are 12 total parts (2 + 5 + 5 = 12).  

We divide 180° by 12 to determine how much each part is of the triangle.

    180°/12   =  15°

So each part is 15°.

The first angle is 2 parts, so 15°(2)  =  30°

The next two angles are both 5 parts, so 15°(5) = 75°

So the angles are  30°, 75°, and 75°

Check your work:  We can see that 30° + 75° + 75° = 180°, so we know we have the right answer!