Answer:
Angle A = 41, Arc CE = 42, Angle C = 41, Angle D = 40, Angle ABE = 61
Step-by-step explanation:
Angle A = Arc BD/2 (Inscribed Angle)
Angle A = 82/2
Angle A = 41
Arc CE = 2 x Angle CEB (Inscribed Angle)
Arc CE = 2 x 21
Arc CE = 42
Angle C = Arc BD/2 (Inscribed Angle)
Angle C = 82/2
Angle C = 41
Angle D = Arc AC/2 (Inscribed Angle)
Angle D = 80/2
Angle D = 40
Angle ABE = Arc AE/2
Angle ABE = Arc AC + Arc CE/2
Angle ABE = 122/2
Angle ABE = 61
m < A = [tex]39^{0}[/tex] , mCE = [tex]40^{0}[/tex], m < c = [tex]39^{0}[/tex], m < D = [tex]37^{0}[/tex] m < ABE = [tex]57^{0}[/tex]
A circle has a total of 360 degrees all the way around the center, so if that central angle determining a sector has an angle measure of 60 degrees, then the sector takes up 60/360 or 1/6, of the degrees all the way around.
a. m < A = [tex]\frac{1}{2}[/tex] mBD
= [tex]\frac{1}{2}[/tex] × [tex]78^{0}[/tex]
= [tex]39^{0}[/tex]
b. mCE = 2m < CBE
= 2 × [tex]20^{0}[/tex]
= [tex]40^{0}[/tex]
c. m < c = m < A = [tex]39^{0}[/tex]
d. m < D = [tex]\frac{1}{2}[/tex] mAC
= [tex]\frac{1}{2}[/tex] × [tex]74^{0}[/tex]
= [tex]37^{0}[/tex]
e. m < ABE = [tex]\frac{1}{2}[/tex] mAC + [tex]\frac{1}{2}[/tex] mCE
= [tex]37^{0}[/tex] + [tex]20^{0}[/tex]
= [tex]57^{0}[/tex]
Hence, m < A = [tex]39^{0}[/tex] , mCE = [tex]40^{0}[/tex], m < c = [tex]39^{0}[/tex], m < D = [tex]37^{0}[/tex] m < ABE = [tex]57^{0}[/tex]
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