Answer
The angle we need to find is 52 degrees.
Work Step by Step
Let X represent the angle we need to find.
The supplement of this angle is 180 - X.
The complement of this angle is 90 - X.
We know that the supplement of the angle is 14 more than three times the complement of the angle.
Three times the complement of the angle means 3 $\times$ (90 - X) = 270 - 3X.
14 more than three times the complement of the angle means 270 - 3X + 14 = 284 - 3X.
The supplement of the angle is 284 - 3X. Also, it is 180 - X. So, we solve the following equation:
284 - 3X = 180 - X
104 = 2X
Divide both sides by 2:
X = 52
The angle we need to find is 52 degrees.
