To find the reference angle of \( 105^\circ \), we first need to understand that the reference angle is the acute angle (less than \( 90^\circ \)) between the terminal side of the given angle and the x-axis.

Since \( 105^\circ \) is in the second quadrant (between \( 90^\circ \) and \( 180^\circ \)), the reference angle is calculated as:

\[
\text{Reference angle} = 180^\circ - \text{given angle}
\]

For \( 105^\circ \):

\[
\text{Reference angle} = 180^\circ - 105^\circ = 75^\circ
\]

So, the reference angle of \( 105^\circ \) is \( 75^\circ \).

Would you like further details or clarifications? 

Here are 5 related questions:
1. How do you find the reference angle for an angle in the third quadrant?
2. What is the reference angle of \( -60^\circ \)?
3. How do reference angles relate to trigonometric functions?
4. How do you find the reference angle for an angle greater than \( 360^\circ \)?
5. What is the reference angle of \( 220^\circ \)?

**Tip:** Remember, the reference angle is always positive and less than \( 90^\circ \).

Learn how to find the reference angle of 105°. A detailed explanation of how reference angles are calculated for angles in different quadrants, including step-by-step guidance on how to find the reference angle for 105°, which lies in the second quadrant. Suitable for high school students (Grades 9-12).

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