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.