How to Bisect an Angle Step-by-Step in Geometry

To bisect an angle with compass and straightedge, draw an arc across both rays, then equal arcs from each crossing point. The line from the vertex through where those arcs meet splits the angle exactly in half.

• A straightedge or ruler.
• A compass.
• A pencil.

Worked examples: bisecting an angle

Practice questions on angle bisection

1. After bisecting ( angle XYZ ), if ( angle XYW = 40^circ ), what’s the measure of ( angle WYZ )?
2. Why is angle bisector important in the construction of the incenter of a triangle?
3. If you bisect a right angle, what type of angles do you get?

1. Since ( angle XYW ) is half of ( angle XYZ ), ( angle WYZ ) will also measure (40^circ).
2. The incenter of a triangle is the point where the angle bisectors of the triangle intersect. It’s equidistant from all the triangle’s sides. This equidistance property is important for inscribing a circle inside the triangle, known as the incircle.
3. You get two acute angles, each measuring (45^circ).

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