Heeey Who Wants To Save My Grade?

[USSRGirl]

Somebody help me solve this wretched geometry problem???

Given: In circle with center O arc BAC = 314 degrees. Find angle A.



Care to find the answer for me?
Bless you son....

[Puritan]

Hmmm. I will try to guide you a bit. Firstly, what number of degrees are in a circle? Take that number and subtract the size of arc BAC to find the size of arc BC. From that information you should be able to determine the size of angle BOC. Now, a flat line is an angle of how many degrees? If you know the size of angle BOC and how many degrees are in a line, you should be able to find the size of angle BOA. Now, things get a little tricky. You know line OB is the same length as line OA as both are straight lines from the center of the circle to point O. Thus you have an isosceles triangle. This indicates a relationship between angle BAO (you call it angle A) and angle ABO. As you should know the number of degrees in all of the angles of a triangle and the number of degrees in angle BOA, you should be able to determine the size of angle A.

[Icarus]

Now, things get a little tricky. You know line OB is the same length as line OA as both are straight lines from the center of the circle to point O. Thus you have an isosceles triangle. This indicates a relationship between angle BAO (you call it angle A) and angle ABO. As you should know the number of degrees in all of the angles of a triangle and the number of degrees in angle BOA, you should be able to determine the size of angle A.

Short version: If the angleis located in the center of the circle, the measure is that of the arc. If it is located on the circle, the measure of the angle is half that of the arc.

As an example, the exterior angle at BOC is 314 degrees, the same as the arc.
The exterior of BAC is 157 degrees.


Good luck.