Alright, let's break this down into really simple terms! Imagine you have two friends, and when you add up their ages, you get a special number every time. That special number is like how much all the angles in a full circle add up to, which is 180 degrees.
Now, let's talk about these two friends: Angle A and Angle B. They are special because when you add up their ages (or angles), you always get 180 degrees because they are 'supplementary' to each other. So, if Angle A is 106.6 degrees less than Angle B, we need to figure out the ages of these friends.
Let's use an easy equation to help us: Angle A + Angle B = 180 degrees. Since we know that Angle A is 106.6 degrees less than Angle B, let's say that Angle A = x degrees. This means that Angle B = x + 106.6 degrees.
Now, we can substitute these values into our equation: x + (x + 106.6) = 180. By solving this equation, we can find the values of Angle A and Angle B. Once we find these values, we will know the measure of each angle!
So, by solving the equation x + (x + 106.6) = 180, we find that Angle A is 36.7 degrees and Angle B is 143.3 degrees. Therefore, Angle A measures 36.7 degrees, and Angle B measures 143.3 degrees. They are like best friends whose ages add up to be 180 years old, just like how their angles add up to a full circle! I hope this helps you understand how to find the measure of each angle when one is 106.6 degrees less than its supplementary angle. Let me know if you need more help!