Find the measure of the complementary angle of the supplementary angle of the angle having measure 120 degree. Want it with full explanation
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60 degrees!

Step-by-step explanation: So, a supplementary angle is an angle of 180 degrees. I'm not sure if you used the incorrect terminology because a complementary angle is an angle that adds up to 90 degrees, which would make this question unsolvable! However, the correct word you are looking for would be the supplement of the angle 120. Get it, supplementary, supplement. Anyways, the supplement is essentially an angle that when added to another angle it will equal 180! In this case, the other angle is 120. We can model this with an equation.

180 - 120 = x

Now before we get confused let's make sure we understand the equation. Our total angleage will equal 180 degrees, so we start off with 180, we then take the measure of the angle we already know which is 120, and subtract it, because if you have 1/4 of a pie somebody already ate the other 3/4, but at one point it was 4/4 or a whole pie, so in this situation, we are taking away 120 degrees of the whole pie, or 180 degrees. This will give us a value of x, or the supplement angle of 120 degrees, which might also be known as the other 1/4 of our pie. When we solve the equation 180-120 we are given the answer 60 degrees! This is what we would call the supplement to our angle 120, or the angle that when added to it, will make it a full 180 degrees. Now, these two angles can also be referred to as supplementary in the context of talking about the two, where you might say 120 and 60 are supplementary angles.

Further not, if you are talking about finding the complement of an angle, or an angle that when added to another angle will give you 90 degrees, the process is exactly the same except the equation would be modeled

90 - y = x

in this case, y is the angle we are given, let's say it's 20, and x is our complement or the angle that when added to 20 will make it 90! The answer to this one is 70 but hopefully, you understand by now!