Tim M. answered • 10/13/19

Industry professional passing on tools for success

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.