Problem: If an angle is 30′ more than one half of its complement, find the measure of the angle.

Understanding the problem:
- An angle and its complement add up to 90 degrees.
- We need to find the measure of the angle.

Let's solve the problem step by step:

Step 1: Understand the given information
- An angle is 30′ more than one half of its complement.

Step 2: Express the information mathematically
- Let the angle be represented by 'x'.
- The complement of the angle is represented by '90 - x'.
- One half of the complement is represented by '(90 - x)/2'.
- According to the given information, the angle 'x' is 30′ more than one half of its complement, which can be expressed as:
x = (90 - x)/2 + 30

Step 3: Simplify and solve the equation
- Distribute 1/2 to (90 - x): x = (90 - x)/2 + 30
- Simplify the equation: 2x = 90 - x + 60
- Combine like terms: 2x + x = 90 + 60
- Simplify further: 3x = 150
- Divide by 3 to solve for x: x = 50

Step 4: Interpret the solution
- The measure of the angle is 50 degrees.

Conclusion:
- The measure of the angle is 50 degrees.

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