Tanya has a triangular garden bed in her back yard. the measure of the largest angle is 30° less than twice the measure of the smallest, and the middle angle is 10°more than the measure of the smallest angle. find the measures of all 3 angles.

The properties of triangles says the total of all three angles will always be 180 degrees. We can use this property to help build our equation for the problem.
Let l be the largest angle, m be the middle, and s be the smallest.
We know from the question that and that .
From the property above, we know .
We then know . From this, we can solve for s, and then plug that value into the equations above for l and m to find them.
Expand the parenthesis and combine like terms.

Add 20 to each side.

Divide both sides by 4.

So, our smallest angle is 50. Now recall the two equations for l and m above and .
Plug in the value of s.

Multiply 2(50).

Subtract 30.

The value of the largest angle is 70.
Plug in the value of s.

Add 10.

Finally, the middle angle is 60. So the answers are l = 70, m = 60, and s = 50.