Answer:
1). m∠ACB = 20°
2). central angle measure = 156°
inscribed angle measure = 78°
circumscribed angle measure = 24°
Step-by-step explanation:
1). Measure of ∠AOB = 40°.
Since m∠ACB = [tex]\frac{1}{2}(m\angle AOB)[/tex]
m∠ACB = [tex]\frac{1}{2}\times 40[/tex]
= 20°
2). Measure of the central angle of the the given circle, m ∠BOD = 156°
Inscribed angle, m∠BAD = [tex]\frac{1}{2}(m\angle BOD)=\frac{1}{2}\times 156[/tex]
= 78°
Circumscribed angle m∠BCD = [tex]\frac{1}{2}(m\widehat{BAD}-m\widehat{BD})[/tex]
= [tex]\frac{1}{2}[(360-156)-156][/tex]
= [tex]\frac{1}{2}(204-156)[/tex]
= [tex]\frac{1}{2}(48)[/tex]
= 24°
Therefore, central angle measure = 156°
inscribed angle measure = 78°
circumscribed angle measure = 24°
