Question

o is the center of the circle. aob =110° . find m(arc AMB)
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Answer 1

Step-by-step explanation:

Given,

angle at centre ∠AOB=110

o

angle at circumference ∠ACO

Now,

we know that the angle at the centre is twice the angle at the circumference subtended by the same arc.

Therefore,

∠AOB=2∠ACO

⟹110

o

=2∠ACO

⟹∠ACO=

2

110

o

=55

o

Now,

∠COA+∠AOB=180

o

⟹∠COA=180

o

−110

o

=70

o

In△AOC,

∠AOC+∠ACO+∠CAO=180

o

⟹70

o

+55

o

+∠CAO=180

o

⟹∠CAO=55

o

Answer 2

Step-by-step explanation:

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