Answer:
The largest angle has a measure of 96 degrees.
Step-by-step explanation:
In order to solve this problem, we have to know the fact that the sumatory of the internal angles of any triangle is 180 degrees.
With this statement in mind, and looking at the image, we can say:
180 = A + B + C (eq. 1)
Before continue any further, let's affirmt that B is the smallest angle.
Now the enunciate says "One angle in a triangle has a measure that is three times as large as the smallest angle"; This can be express as:
A = 3B (eq. 2)
The other enunciate is "The measure of the third angle is 20 degrees more than that of the smallest angle" This can be express as:
C = B + 20 (eq. 3)
Now, replacing equations 2 and 3 into 1:
(eq. 1) 180 = 3B + B + B + 20
And clearing B:
B = 32.
By knowing B, we can clear A and C from equations 2 and 3 respectively:
(eq. 2) A = 3B, so A= 96
(eq. 3) C = B + 20, so C =52
