Answer:
16) m arcABC = 135°
17) m arcBCD = 135°
18) m arcDE = 135°
19) m∠AOE = 45°
20) m∠BCE = 45°
21) m∠ECD = 67.5°
22) m∠ADC = 67.5°
Step-by-step explanation:
Since line segAD is a diameter, then it is 180°
line segAD = ∠AOB+∠BOC+∠COD
180° = x+2x+x
x = 180°÷4 = 45°
All chords are radii, thus all angles are central angles. The measure of intercepted arc and of the central angle are the same:
∠AOB = arcAB = 45°
∠BOC = arcBC = 2x = 90°
∠COD = arcCD = 45°
16) arcABC = arcAB+arcBC
= 45°+90°
arcABC = 135°
17) arcBCD = arcBC + arcCD
= 90°+45°
arcBCD = 135°
Since line segCE is also a diameter, then it is 180°.
line segCE = ∠COD+∠DOE
180° = 45°+∠DOE
∠DOE = 180°-45°
∠DOE = 135°
18)∠DOE = arcDE = 135°
19)∠AOE = 180°-135° = 45° OR ∠COD = ∠AOE since line seg AD intersects with line segCE.
20) ∠BCE = 1/2 arcBE
= 90/2
∠BCE = 45°
21) ∠ECD = 1/2 arcDE
= 135/2
∠ECD = 67.5°
22) ∠ADC = 1/2 arcABC
= 135/2
∠ADC = 67.5°
