Question

How do you find related acute angles?

Answer 1

Hint: since we have been told to find the related acute angle in the question, try to define acute angle and related acute angle first. You will get to know the difference between both of them and hence it will further make it easy to find the related acute angle from any measurement of angle.

Complete step by step answer:
An angle which is $<{90}^{\circ }$ (less than 90) is called a cute angle. Now a related acute angle is defined as the acute angle which is formed by the x-axis and the terminal side only when the terminal side is in the 2-quadrant, 3-quadrant and the 4-quadrant. A terminal side is the other side of the angle the other side of the angle other than the fixed side of an angle.

For example side PO is the terminal side of $\mathrm{\angle }POQ$ and side OQ is the fixed side in the above figure.
Now the principal angle is the angle formed by the positive x-axis and the terminal side in an anticlockwise direction. To find the related acute angle one should follow the given steps:
1.If the terminal side lies in the 2-quadrant, subtract the principle angle from ${180}^{\circ }$. This will give us the related acute angle.
2.If the terminal side lies in the 3-quadrant, subtract ${180}^{\circ }$ from the principal angle.
3.If the terminal side lies in the 4-quadrant, subtract the principle angle from ${360}^{\circ }$ to find the related acute angle.

Note: For solving these types of questions the only thing you need to know is the definition correctly. The value of the related acute angle will always measure between $0^{\circ }$ and ${90}^{\circ }$ even if it is present in any of the four quadrants. If the related acute angle is counted in an anti-clockwise direction it will always be positive.