Question
What are the other angles that can be constructed using angle bisection? Can you construct a 65.5° angle?
✓
Answer
By using the angle bisector method, we can bisect any given angle.
Using a ruler and compass, we know the method of making a 90° angle on a line.
We have $\frac{90}{2}=45$ and $\frac{45}{2}=22.5^{\circ}$.
∴ By using an angle bisector, we can make angles of 45° and 22.5°.
Also, 90° + 45° = 135°, 90° + 22.5° = 112.5°, 45° + 22.5° = 67.5°.
∴ We can also construct angles 135°, 112.5°, and 67.5° using the angle bisector.
∴ By using angle bisector, we cannot construct angle of 65.5°.
Using a ruler and compass, we know the method of making a 90° angle on a line.
We have $\frac{90}{2}=45$ and $\frac{45}{2}=22.5^{\circ}$.
∴ By using an angle bisector, we can make angles of 45° and 22.5°.
Also, 90° + 45° = 135°, 90° + 22.5° = 112.5°, 45° + 22.5° = 67.5°.
∴ We can also construct angles 135°, 112.5°, and 67.5° using the angle bisector.
∴ By using angle bisector, we cannot construct angle of 65.5°.
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