A) ∠A intercepts arc CD.
B) ∠BED intercepts arc BCD.
C) The measure of an inscribed angle is half the measure of its intercepted arc. So...
The measure of ∠BED is half the measure of arc BCD
The measure of ∠BED = (1/2)(the measure of arc BCD)
85° = (1/2)(the measure of arc BCD)
2(85°) = the measure of arc BCD
170° = the measure of arc BCD
D) The measure of ∠A = (1/2)(the measure of arc CD)
The measure of ∠A = (1/2)(128°)
The measure of ∠A = 64°
E) The sum of all the arcs in a circle is 360° , so...
The measure of the rest of the circle = 360° - 82°
The measure of the rest of the circle = 278°
A) ∠A intercepts arc CD.
B) ∠BED intercepts arc BCD.
C) The measure of an inscribed angle is half the measure of its intercepted arc. So...
The measure of ∠BED is half the measure of arc BCD
The measure of ∠BED = (1/2)(the measure of arc BCD)
85° = (1/2)(the measure of arc BCD)
2(85°) = the measure of arc BCD
170° = the measure of arc BCD
D) The measure of ∠A = (1/2)(the measure of arc CD)
The measure of ∠A = (1/2)(128°)
The measure of ∠A = 64°
E) The sum of all the arcs in a circle is 360° , so...
The measure of the rest of the circle = 360° - 82°
The measure of the rest of the circle = 278°