Question 904923: Solution with answer please thank you!
Find the angles of a triangle where the smallest angle is 36° smaller than the next larger angle, and the larger angle is 111° larger than the smallest angle.
Answer by AlgebraLady88(44)   (Show Source):
You can put this solution on YOUR website! We know that all angles in a triangle will equal 180 degrees.
So, let's start.
We read that the smallest angle is 36 degrees smaller than the next larger angle.
So, we will name the next larger angle, L. This makes the smallest angle L-36.
We now have two angles already : the smallest angle = L-36
the next larger angle = L
So, what about the larger angle? This would be the largest angle here as there are only three angles in a triangle. We are told that the larger angle is 111 degrees larger than the smallest angle.
We remember that the smallest angle is L-36
So, the largest angle is (L-36) + 111
So, now we have our equation below:
L + ( L-36) + (L-36) + 111 = 180
L + L - 36 + L -36 + 111 = 180
3L + 39 = 180
3L = 180- 39
3L = 141
L = 47
So, L= 47 degrees , the smallest angle would be (L-36) = 11 degrees and the largest angle would be (L-36)+111 = 122 degrees.
To check,
47 + 11 + 122 = 180 degrees
|
|
|
