28. Which angle in standard position has a reference angle of 62 degrees?

a) 28

b) 152

c) 242

d) 332

To determine which angle in standard position has a reference angle of 62 degrees, we need to understand that the reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. The reference angle is always between 0 and 90 degrees.

Angles with a reference angle of 62 degrees can be found in the following quadrants:

1. **Quadrant I**: The angle itself is the reference angle. So, the angle is 62 degrees.
2. **Quadrant II**: The angle is \(180^\circ - 62^\circ = 118^\circ\).
3. **Quadrant III**: The angle is \(180^\circ + 62^\circ = 242^\circ\).
4. **Quadrant IV**: The angle is \(360^\circ - 62^\circ = 298^\circ\).

Given the options:

a) 28 degrees  
b) 152 degrees  
c) 242 degrees  
d) 332 degrees  

The angle with a reference angle of 62 degrees is:

c) 242 degrees

Would you like more details or have any questions? Here are five more questions you might consider asking:

1. How do you find the reference angle for any given angle?
2. What are the properties of angles in different quadrants?
3. How do you convert degrees to radians?
4. How do you find the sine, cosine, and tangent of an angle?
5. What is the unit circle and how is it used in trigonometry?

**Tip:** When solving for angles in different quadrants, always consider the relationship of the angle with the nearest x-axis to find the reference angle.

Explore which angle in standard position has a reference angle of 62 degrees. Understand how to identify angles and their reference angles in different quadrants. Suitable for high school students studying trigonometry.

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