triangle YRC is iscocles, YR and RX are both radius, so they are equal.
So the base angles must be equal as well.
we know that the central angle is 68, because arc YX is 68.
to find the measure of angle C use the equation 2x+68=180 (2 of the same angle (x) + 68 makes all the angles in the triangle.
2x=180-68
2x=112
x=56
Skip E until the end
<G is 84
<G and the angle that is 96 make a linear pair
<G + 96=180
<G=84
Arc YS is 112
Arc YS is = <R
find <R
<R and the angle across from ARC YX are a linear pair
<YRX is 68
<R+68=180
<R is 112
<D and F are 42
<D and <F are the base angles of an isosceles triangle (2 sides are the radius again)
the central angle in this case is 96
2x+96=180
2x=84
x= 42
so both D and F are 42
now <E is 96
measure of an angle outside the circle with 2 rays touching the circle is the measure of the larger arc of the circle minus the smaller arc divided by 2
