He measure of an angle is 78° less than the measure of its complement. what is the measure of the angle?

When we say two angles are complementary, we mean that they add up to a right angle – 90 degrees. Now, we haven’t been given either of the angles directly, but we’ve been given their relationship, and we’ve been given the fact that they’re complementary. If we call the angle’s complement θ, we can express the fact that our angle is 78 degrees less than that with the expression (θ-78). Putting our information together, we have:

θ+(θ-78)=90
2θ-78=90

From there, it’s fairly straightforward algebra; just solve for θ. Remember though, the answer they’re looking for is the (θ-78) term, so make sure to evaluate that once you’ve found θ.