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Describing Angles

We will start this exercise by copying the angle. Then we will bisect it.

Copying the angle

In the exercise, we are given an angle to copy.

We shall begin by using a straight-edge to draw a ray.

Next we put the point of the compass on the vertex of the given angle, and then draw an arc passing through both rays. We then place the point of the compass at the starting point of the arc we drew. With this point as our center, we draw an arc similar to the one we made on the given angle.

Go back to the angle that was given and identify the points where the arc passes through each ray. Use the compass to measure this distance.

Return to the angle we are constructing, preserving the length that we measured with the compass. Place the point of the compass where the arc intersects the ray. Use the compass to make a mark on the arc as seen below.

From the starting point of our ray through the intersection point we just made, draw a new ray to form the angle.

We have now copied the angle.

Keep the arc that was made when copying the angle as we will need it to bisect the angle.

Bisecting the angle

The first step to bisect the angle is to place the point of the compass at one a point where the arc intersects one of the rays. We draw an arc in the space between the rays using a measure than spans more than half of the angle.

We keep the compass fixed at this distance and move the point to the where the first arc crosses the other ray. We draw a third arc in the space between the rays that intersects the second ray.

The last step when we create the angle bisector is to draw a ray from the vertex of the angle through the point where the second and third arcs intersect.

We have now bisected the angle and it looks like this.