Two angles are complementary. the sum of the measures of the first angle and half the second angle is 64°. find the measures of the angles

One angle is 52 degrees, and the other is 38 degrees.

Step-by-step explanation:

First, I transcribed the given sentences into equations.

The first sentence says that "Two angles are complementary".

Let's call the first angle x and the second angle y. If two angles are complementary, then their sum is 90 degrees. So we know that x + y = 90.

The second sentence says that "The sum of the measures of the first angle and half the second angle is 64°".

x + y/2 = 64

Then we can use the elimination strategy to solve for one of the variables. In this case, it is easier to subtract the second equation from the first to eliminate x.

  x + y = 90

-  x + y/2 = 64

y/2 = 26 ==> y = 52

Now that we know that y = 52, we can substitute that back into the first equation, and get x + 52 = 90, so x = 38.

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