Question

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.

Answer 1

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
`l = 2s - 30` and that
`m = s + 10`.
From the property above, we know
`l + m + s = 180`.
We then know
`(2s - 30) + (s + 10) + s = 180`. 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.

`4s - 20 = 180`
Add 20 to each side.

`4s  =  200`
Divide both sides by 4.

`s  =  50`
So, our smallest angle is 50. Now recall the two equations for l and m above
`l = 2s - 30` and
`m = s + 10`.
Plug in the value of s.

`l = 2(50) - 30`
Multiply 2(50).

`l = 100 - 30`
Subtract 30.

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

`m = 50 + 10`
Add 10.

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