Imagine there are two angles that when added together equal a right angle, which is 90 degrees. Let's call one angle x degrees and the other y degrees. So, x + y = 90 degrees. The problem tells us that the measure of one angle is three times the other. Since we have two angles adding up to 90 degrees and one angle is three times the other, we can set up an equation: x = 3y.
Now, we can substitute x = 3y into the equation x + y = 90. This gives us 3y + y = 90, which simplifies to 4y = 90. To find the value of y, we divide both sides by 4: y = 90 / 4 = 22.5 degrees. Now that we have the value of y, we can find x using x = 3 * 22.5 = 67.5 degrees.
Therefore, one angle is 67.5 degrees and the other angle is 22.5 degrees. These two angles are complementary, meaning they add up to 90 degrees. This concept can be shown visually by splitting a right angle into two parts where one part is three times the size of the other.
In summary, the measure of an angle being three times the measure of its complementary angle can be understood by setting up equations, solving for the unknown angles, and visualizing the relationship between the angles in a right angle.
Through this step-by-step explanation and practical examples, we can see how to determine the measure of each angle when their relationship is based on being complementary and one angle being three times the other.