We know that with an angle ∠A we can construct its bisector that will divide it into two equal angles whose measure is 21m∠A. If we divide one of these angles into two equal angles, we will get an angle whose measure is as follows.
21⋅21m∠A=41m∠M
This is what we want! Let's construct it! We begin by drawing ∠A.
Now we can construct an angle bisector by putting a compass on the vertex, drawing an arc that intersects the sides of ∠A, and then drawing two intersecting arcs from the points of intersection with the same compass setting. Finally, we can draw a ray from the vertex through the point of intersection as shown below.
We call one of these angles whose measure is 21m∠A as 21A. Now, we can construct an angle bisector of ∠21A! To do it, we follow the sames steps as constructing an angle bisector of ∠A.
We constructed an angle ∠41A, whose measure is 41m∠A. Now we can answer the questions from the exercise.
How is the angle ∠41A related to the angle bisector of ∠A?
As we can see, one of the sides of ∠41A is the angle bisector of ∠A.
How can you use previous constructions to help you?
To construct the angle ∠41A, we constructed the angle bisector of ∠A first. It helped us find an angle whose measure is 41m∠A.
Mathleaks uses cookies for an enhanced user experience. By using our website, you agree to the usage of cookies as described in our policy for cookies.
