Let's start with what's not explicitly mentioned in the question:
When two angles add to 90º, they are complements.
We can write this like so:
a + b = 90
Where a is the measure of the first angle, and b is the measure of the second.
In our question, we're told that the complement of an angle (we'll make it a), is 14 more than 3 times the angle itself (which we'll make b).
We can write this like so:
a = b * 3 + 14
For problem a, we can plug the value of a into the complement equation like so:
a + b = 90
(b * 3 + 14) + b = 90
Combine like terms:
4b + 14 = 90
Subtract 14 from both sides to remove the 14 on the left:
4b = 76
Divide both sides by 4 to remove the 4 on the left:
b = 19
The solution to problem a is 19.
For problem b, we can go back to our complement equation and plug our value for 19 in like so:
a + b = 90
a + 19 = 90
Subtract 19 from both sides to remove the 19 on the left:
a = 71
The solution to problem b is 71.
We can check our work on b by plugging in the values that we have for a and b into the equation for the value of a.
a = b * 3 + 14
71 = 19 * 3 + 14
Multiply the 19 and 3:
71 = 57 + 14
Add the 57 and 14:
71 = 71
So those two are correct and verified!
For problem c, the supplement of an angle is the difference between 180 and that angle.
We can write this like so:
x + y = 180
We can plug in our answer from problem a:
19 + y = 180
Subtract 19 from both sides:
y = 161
The solution to problem c is 161.
