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in circle O, AD and CE are diameters

show ur solution​

In Circle O AD And CE Are Diametersshow Ur Solution class=

Sagot :

Onlyakemidn

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°

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