Problema Solution
In a triangle the measure of the middle angle is 9 degrees less than twice the measure of the smallest angle. The largest angle is 37 degrees more than the measure of the smallest angle. What are the measures of the three angles ?
Answer provided by our tutors
Let a, b and c represent the measures of the three angles and let a<b<c
a + b + c = 180
The measure of the middle angle is 9 degrees less than twice the measure of the smallest angle:
b = 2a - 9
The largest angle is 37 degrees more than the measure of the smallest angle:
c = 37 + a
We have the following system of equations:
a + b + c = 180
b = 2a - 9
c = 37 + a
........
........
a = 38 degrees
b = 67 degrees
c = 75 degrees
The measures of the angles are: 38 degrees, 67 degrees and 75 degrees.