MathDB

Point

A,B,C,D,

and

E

are equally spaced on a minor arc of a circle. Points

E,F,G,H,I

and

A

are equally spaced on a minor arc of a second circle with center

C

as shown in the figure below. The angle

\angle ABD

exceeds

\angle AHG

12^\circ

. Find the degree measure of

\angle BAG

.[asy] pair A,B,C,D,E,F,G,H,I,O; O=(0,0); C=dir(90); B=dir(70); A=dir(50); D=dir(110); E=dir(130); draw(arc(O,1,50,130)); real x=2*sin(20*pi/180); F=x*dir(228)+C; G=x*dir(256)+C; H=x*dir(284)+C; I=x*dir(312)+C; draw(arc(C,x,200,340)); label("

A

",A,dir(0)); label("

B

",B,dir(75)); label("

C

",C,dir(90)); label("

D

",D,dir(105)); label("

E

",E,dir(180)); label("

F

",F,dir(225)); label("

G

",G,dir(260)); label("

H

",H,dir(280)); label("

I

",I,dir(315)); [/asy]

Problem Statement