Question

Using this fact draw an angle of measure 37¹/2 in different ways on a paper​

Answer 1

Answer:

Here is your answer ♦♦

Step-by-step explanation:

Say you wanted to construct an angle of 37.5 degrees at endpoint B of AB.

Draw AB of required length.

1. At B, with any radius, draw a semicircle.
2. Without changing the radius, place your compass tip on the point where the semicircle and AB intersect, and cut an arc on the semicircle. Again, without changing the radius, place the tip of your compass where this new arc intersects the semicircle. Essentially you have trisected a semicircle, thus forming angles 60 deg and 120 deg.
3. Bisect 0 deg and 60 deg, by taking any radius more than half the distance between the two arcs corresponding to 0 deg and 60 deg. You have formed 30 deg.
4. Bisect 60 deg and 120 deg, by taking any radius more than half the distance between the two arcs corresponding to 60 deg and 120 deg. You have formed 90 deg.
5. Bisect 0 deg and 90 deg, by taking any radius more than half the distance between the two arcs corresponding to 0 deg and 90 deg. You have formed 45 deg.
6. Bisect 45 deg and 30 deg, by taking any radius more than half the distance between the two arcs corresponding to 45 deg and 30 deg. You have formed 37.5 deg.
7. Any angle you can construct with a compass, can be obtained by trisection and/or bisection of other angles. Just look for values you can add or subtract to the angle you want to construct, in order to get a more “standard” value. In this case, 37.5 + 7.5 = 45, 37.5 - 7.5 = 30. Both of these are standard angles, and can easily be constructed and then bisected.