Answer: See Below
Explanation:
there is a ton of information here to get through
<a is 34 (half of 68)
<C is 56
- 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
- the measure of the smaller arc is the same as <G
- smaller arc is 84
- the larger arc is 360-84
- the larger arc is 276
- 276-84= 192
- divide by 2 to get <E
- 192/2=96