9514 1404 393
Answer:
(a) 62°
Step-by-step explanation:
Let 'a' represent the angle. Then its complement is (90-a) and its supplement is (180-a). The relation given in the problem statement is ...
(180 -a) = 6 +4(90 -a)
180 -a = 366 -4a . . . . . . . . eliminate parentheses
3a = 186 . . . . . . . . . . add 4a -180
a = 62 . . . . . . . . . divide by 3
The measure of the angle is 62°.
_____
<em>Additional comment</em>
It is just about as easy to solve for the complement of the angle. Of course, the supplement is 90° more than the complement.
x +90 = 6 +4x . . . x is the complement of the angle
84 = 3x . . . . . . . . subtract x+6
28 = x . . . . . . . . . divide by 3
90 -x = 62 . . . . . the angle of interest
