Harrison D. answered • 10/03/22
Princeton Graduate with Outstanding Academic Performances in Math
When we say that two angles are complementary, this means that when the angles are put together as an adjacent pair they form a right angle, or an angle that is 90 degrees. In other words, when we add the measure of two complementary angles together, their sum will always be 90 degrees (by the definition of complementary angles).
Because of this, we can express the relationship between the angles in an algebraic expression (let's say "A" is angle 2 and "B" is angle 3, and each represents the measurement of the angle in degrees):
A + B = 90
Assuming the 57 that you mention for the measure of angle 2 is in units of degrees, we can substitute that value for A (angle 2) in our expression to leave us with one unknown variable – our goal, in fact – B or angle 3:
57 + B = 90
To solve for B, we can then subtract 57 from both sides, leaving us with our answer:
57 + B = 90
-57 -57
B = 33 (degrees)
There you have it! The measure (m) of angle 3 is 33 degrees, which we know from the definition of complementary angles as making a sum of 90 degrees, and subtracting the angle whose value we know (angle 2) that represents one part of the total.
