Angle(D) cuts off arc(ABC) ---> angle(D) = ½·arc(ABC)
Angle(B) cuts off arc(ADC) ---> angle(B) = ½·arc(ADC)
Since arc(ABC) + arc(ADC) creates the whole circle: arc(ABC) + arc(ADC) = 360o
Therefore: angle(D) + angle(B) = ½·arc(ABC) + ½·arc(ADC)
= ½·( arc(ABC) + arc(ADC) )
= ½·( 360o )
= 180o
---> (x + 24)o + (x + 10)o = 180o
---> 2xo + 34o = 180o
---> 2xo = 146o
---> xo = 73o
Now, find the sizes of angle(A), angle(B), and angle(D).
Add these values together and subtract from 360o to find the size of angle(C).