Problem Solving Series 101: Angles

Problem solving with angles is very easy, we just to have to convert the word into mathematical equation and solve it as normal. If you already know how to do it, then you are good to go. If not, take a glance, familiarize of the technique and come back later if you think you can deal with it without looking at the solution.

What do you need to know?

1. The sum of complementary angles is equal to 90°. This means that the complement of angle x is 90-x.

2. The sum of the supplementary angles is equal to 180°. This means that supplement of the angle x is 180-x.

Let’s Practice! Check the problem, write solution your and compare your answer.

Worked Problem 1:

Find the supplement of the complement of 35º.


Let’s cut the problem into two. First, complement of 35º which is 90-35=55º.

Now, the supplement of 55º which is 180-55=125º.

Worked Problem 2:

Two angles are supplementary. On angle is 24º less than thrice the other angle. What is the complement of the smaller angle?


First and foremost is to represent the angle as variable.

Let x: be the first angle

180-x: the other angle since they are supplementary

Converting this phrase “One angle is 24 less than thrice the other angle” to mathematical equation we have,






Therefore the other angle 180-117=63º.

But the question is the complement of the smaller angle. That is 90-63=27º.

Worked Problem 3:

If \angle X=(6+5k), and \angle Y=(158-3k) both in degrees, are supplementary. Find the complement of angle X.


\angle X+\angle Y=180





Solving for angle X.

\angle X=6+5(8)

\angle X=46

The complement of 46 is 90-46=44º.


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