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Find <ABC + <ADC
help... ASAP! :)​

Find <ABC + <ADC help... ASAP! :)​-example-1

1 Answer

3 votes

Answer:

Option D. 124°

Explanation:

step 1

Find the measure of angle AOC

The triangle AOC is an isosceles triangle, because OA=OC=radius

so


m\angle OAC=m\angle OCA=28^o

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees


m\angle OAC+m\angle OCA+m\angle AOC=180^o

substitute the given values


28^o+28^o+m\angle AOC=180^o


56^o+m\angle AOC=180^o


m\angle AOC=180^o-56^o


m\angle AOC=124^o

step 2

Find the measure of arc AC

we know that


arc\ AC=m\angle AOC ----> by central angle

we have


m\angle AOC=124^o

therefore


arc\ AC=124^o

step 3

we know that

The inscribed angle is half that of the arc comprising


m\angle ABC=(1)/(2)[arc\ AC]


m\angle ADC=(1)/(2)[arc\ AC]

so


m\angle ABC=m\angle ADC

therefore


m\angle ABC+m\angle ADC=2m\angle ABC=arc\ AC

substitute the value of the arc AC


m\angle ABC+m\angle ADC=124^o

User Barett
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