"Half the measure of the angle is 25 more than one third the measure of the complement. Find the angle" I don't understand how to set up and solve this at all.

If x is the angle, 90-x is the complement. So, changing the words to math, you have

x/2 = 25+(90-x)/3

Now just find x.

To set up and solve this problem, we can follow these steps:

Step 1: Understand the problem.
Let's begin by assigning variables to the unknown quantities in the problem.
Let 'x' represent the angle whose measure we are trying to find.
The complement of this angle is 90 degrees - x degrees.

Step 2: Translate the given information into an equation.
We are told that "half the measure of the angle is 25 more than one third the measure of the complement." Converting this sentence into an equation, we get:

(1/2)x = (1/3)(90 - x) + 25

Step 3: Solve the equation for x.
To solve the equation, we'll start by simplifying both sides. Multiplying both sides of the equation by 2 and 3 to eliminate the fractions, we have:

2 * (1/2)x = 2 * [(1/3)(90 - x) + 25]

x = (2/3)(90 - x) + 50

Next, distribute the 2/3 through the parentheses:

x = (2/3)(90) - (2/3)x + 50

Simplify further:

x = 60 - (2/3)x + 50

Combine like terms:

x + (2/3)x = 110

(5/3)x = 110

Now, isolate x by multiplying both sides by 3/5:

(3/5)(5/3)x = (3/5)(110)

x = 66

Step 4: Check the answer.
To verify our answer, substitute x = 66 into the original equation:

(1/2)x = (1/3)(90 - x) + 25

(1/2)(66) = (1/3)(90 - 66) + 25

33 = (1/3)(24) + 25

33 = 8 + 25

33 = 33

The equation holds true, which confirms that the answer, x = 66, is correct.

Therefore, the angle measures 66 degrees.

To set up and solve this problem, let's break it down step by step:

Step 1: Understand the problem
We are given a certain relationship between the measure of an angle and its complement. The problem states that "Half the measure of the angle is 25 more than one-third of the measure of the complement." This can be written as an equation.

Step 2: Assign variables
Let's assign a variable to represent the measure of the angle. We can use 'x' for this. The complement of the angle can be represented by 90° - x, as the sum of an angle and its complement is always 90°.

Step 3: Translate the problem statement into an equation
According to the problem, "Half the measure of the angle is 25 more than one-third of the measure of the complement." This can be translated into an equation as:

(1/2) * x = (1/3) * (90 - x) + 25

Step 4: Solve the equation
To solve this equation, we can start by simplifying both sides. First, distribute (1/3) to (90 - x):

(1/2) * x = (30 - (1/3) * x) + 25

Next, let's combine like terms:

(1/2) * x = 55 - (1/3) * x

To eliminate the fractions, we can multiply every term by 6 (the least common multiple of 2 and 3):

6 * (1/2) * x = 6 * (55 - (1/3) * x)

3x = 330 - 2x

Now, let's isolate x by getting all the x terms on one side:

3x + 2x = 330

5x = 330

To solve for x, divide both sides by 5:

x = 330 / 5

x = 66

Step 5: Find the angle
Now that we have found the value of x, which represents the measure of the angle, we can substitute it back into the equation:

x = 66

Therefore, the measure of the angle is 66 degrees.