The measure of the complement of an angle excites it by 23' . Find the angle 

Let's denote the measure of the angle as \(x\). The complement of an angle is what remains when the angle is subtracted from \(90^\circ\).

The problem states that the complement of the angle exceeds the angle by \(23'\) (minutes). So we can write this relationship as:

\[
(90^\circ - x) = x + 23'
\]

### Step-by-step solution:
1. Start by setting up the equation based on the given relationship:
   \[
   90^\circ - x = x + 23'
   \]

2. Add \(x\) to both sides of the equation to get rid of the negative \(x\) on the left-hand side:
   \[
   90^\circ = 2x + 23'
   \]

3. Subtract \(23'\) from both sides:
   \[
   90^\circ - 23' = 2x
   \]

   Since \(23'\) is in minutes, let's convert \(90^\circ\) into degrees and minutes. \(90^\circ = 89^\circ 60'\), so:
   \[
   89^\circ 60' - 23' = 89^\circ 37'
   \]

4. Now we have:
   \[
   89^\circ 37' = 2x
   \]

5. Divide both sides by 2 to solve for \(x\):
   \[
   x = \frac{89^\circ 37'}{2}
   \]

   Perform the division:
   \[
   x = 44^\circ 48.5'
   \]

So, the measure of the angle is approximately \(44^\circ 48.5'\).

Would you like further details or explanations?

### Related Questions:
1. What is the difference between complementary and supplementary angles?
2. How would the equation change if the complement exceeds the angle by a different amount?
3. What happens when the angle and its complement are equal?
4. How can angles be measured in radians instead of degrees?
5. How do we convert minutes and seconds of an angle into decimal degrees?

**Tip:** Always ensure that the units (degrees and minutes) are consistent throughout your calculations.

The measure of the complement of an angle exceeds it by 23'. Find the angle.

Solve the problem of finding an angle whose complement exceeds it by 23 minutes. This detailed step-by-step solution covers key concepts of complementary angles and basic algebra. Suitable for students in Grades 7-10.

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