Question

http://tinypic.com/view.php?pic=2cgzo6v&s=6

how would i find the measure of angle GAH?

Answer 1

I believe it is a 30 degree angle. You have to see to squares (90 degree angles) an work from there remembering you different rules such as straight lines are 180 deg 180- an angle gives you the adj angle and such

Answer 2

there are 12 equal spaced segments according to the figure description.
let the radius be r.
so perimeter=2pi*r=12arc(GH)
so, arc(GH)=2pi*r/12
let the center of the circle be O.
so, angle(GOH)=X radian
and angle(GAH)=(1/2)angle(GOH)=X/2 radian
Now arc(GH)=r*angle(GOH)=rX
=>rX=2pi*r/12
=>X=pi/6
=>X/2=pi/12=15 degree
so, angle(GAH)=15 degree

Answer 3

Seems like a much easier approach is to use the fact that the angle of an intercepted arc with the vertex on the circle (such as GAH) is half the arc. 360 degrees/12 points = 30 degrees for the arc, so the angle is 15 degrees...

Answer 4

Of course, it's only easier if you remember that property :-)

Answer 5

Perhaps the way to remember is like this:

The arc making up the left half of the circle is 180 degrees, and the angle formed by the two lines is clearly 90 degrees.