Related Topics: More Geometry Lessons

In these lessons, we will learn

**How to draw an angle bisector using a compass and a straight edge?**

1. Place compass point on the vertex, and draw an arc across each ray.

2. Place the compass on each arc intersection and draw a further pair of arcs which intersect each other.

3. Use a straight edge to connect the intersection point to the vertex.**How to bisect a given angle using only a compass and straightedge?**
### Use angle bisector to construct angles

**How to construct 30, 45, 60, 90, and 120 degree angles with a compass by constructing angle bisectors?**
**How to construct a 75° angle by constructing a 60° angle and a 15° angle?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

In these lessons, we will learn

- how to construct an angle bisector of a given angle.
- how to use an angle bisector to construct some angles for example, 90 degrees, 45 degrees, 60 degrees, 30 degrees, 120 degrees, 135 degrees, 15 degrees.

* Example : *Construct an angle bisector for the following angle:

*Solution: *

**Step 1 :** Put the sharp end of your compasses at point *B* and make one arc on the line *BC* (point *S*) and another arc on line *AB *(point *T*).

**Step 2 **: Put the sharp end of the compasses at *S* and make an arc within the lines *AB* and *BC.* Do the same at *T* and make sure that the second arc intersects the first arc.

**Step 3 : **Draw a line from point *B* to the points of intersection of the 2 arcs. This line bisects ∠ABC.

The steps to construct an angle bisector can be summarized as follows:

1. From the vertex, draw an arc across both rays of the angle.

2. From each arc intersection draw another pair of arcs that intersect each other.

3. Draw a line from the vertex to the intersection point to form the angle bisector.

1. Place compass point on the vertex, and draw an arc across each ray.

2. Place the compass on each arc intersection and draw a further pair of arcs which intersect each other.

3. Use a straight edge to connect the intersection point to the vertex.

We can use the angle bisector to construct some other angles from existing angles.

* Example*

A 30˚ angle can be obtained by bisecting a 60˚ angle.

A 15˚ angle can be obtained by bisecting a 30˚ angle.

A 45˚ angle can be obtained by bisecting a 90˚ angle.

A 22.5˚ angle can be obtained by bisecting a 45˚ angle.

*Example: *

The figure shows a point *A* on a straight line. Construct an angle of 45˚ at point *A*.

* Solution: *

Construct a 90˚ angle, and then construct an angle bisector to obtain a 45˚ angle.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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