What is the measure of the angle whose complement is 30 more than twice the angle?

You have a hybrid problem, one that requires a knowledge of algebra and rudimentary geometry. First, you have to know what the complement of an angle is. If the sum of the measures of two angles equals 90 degrees, they are complements. For example, if two angles have measures of 30 degrees and 60 degrees, they are complementary angles. Put another way, you could say that 60 degrees is the complement of 30 degrees, because 90 - 60 = 30. The second thing is far more difficult: you need to figure out a way to set up an algebraic equation from the Words given in the question. Not easy. But let's give it a go. We need to be systematic about it. Let x = "the angle" you are looking for. Let 90 - x = the angle's complement. Let 2x = "twice the angle." And let 2x + 30 = "30 more than twice the angle." Can you see how this is developing? I think we have all the mathematical building blocks -- the Words of the equation -- to match the English Words. Since the complement is 30 more than twice the angle, the equation is 90 - x = 2x + 30 Now, you must use your algebra skills to solve for x. First, add x to both sides of the equation 90 = 3x + 30 Next, subtract 30 from both sides 60 = 3x Now, divide both sides by three 20 = x So, x = 20. Check the answer. Does it make sense? Let's see. If the angle is 20, its complement is 70. Twice the angle is 40. Is 70 thirty more than 40? Yep. Algebra works!