Answer
Angle 1: 93 degrees
Angle 2: 25 degrees
Angle 3: 43 degrees
Angle 4: 68 degrees
Angle 5: 90 degrees
Angle 6: 22 degrees
Angle 7: 68 degrees
Angle 8: 22 degrees
Angle 9: 50 degrees
Angle 10: 112 degrees
Work Step by Step
An inscribed angle is half of the length of the corresponding arc. Thus:
Angle 5 = $.5(180) = 90^{\circ}$
Angle 4 = $.5(136) = 68^{\circ}$
Angle 7 = $.5(136) = 68^{\circ}$
The sum of the measures of angles of a triangle is 180 degrees. Thus:
Angle 8 = $180 - 90 - 68 = 22^{\circ}$
The measure of an angle in the center of the circle is equal to the measure of the corresponding arc. Thus:
Angle 9 = $50^{\circ}$
We find angle 2:
Angle 2 = $180 - .5(50) - 130 = 25^{\circ}$
Thus, we find angle 6:
Angle 6 = $180 - 68 - 90 = 22^{\circ}$
Using the fact that angle ADB equals 65 degrees, we obtain:
Angle 1 = $ 180 - 22 - 65 = 93^{\circ}$
This makes angle 10:
Angle 10 = $ 180 - 43 - 25 = 112^{\circ}$
Finally, we find angle 3:
Angle 3 = $ 180 - 112 -25 = 43^{\circ}$
