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1 Answer
Sean
Jan 31, 2018

Please see below.

Explanation:

.

There is a theorem in geometry that says any angle that has its vertex on the circumference of a circle has a measure equal to half the measure of the arc it is facing (subtended angles).

Therefore:

#/_ABC=(arcADC)/2#

#/_ADC=(arcABC)/2#

#/_ABC+/_ADC=(arcADC+arcABC)/2#

But #(arcADC+arcABC)=360^@# because they add up to the full circumference of the circle.

Therefore,

#/_ABC+/_ADC=360^@/2=180^@#

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