Angle D = ABC arc / 2
x + 100 = ABC arc / 2
ABC arc = 2 × ( x + 100 )
ABC arc = 2x + 200 ( ♡ )
_________________________________
Angle B = ADC arc / 2
3x = ADC arc / 2
ADC arc = 2 × 3x
ADC arc = 6x ( ☆ )
_________________________________
ABC arc + ADC arc = 360
( ♡ ) , ( ☆ ) :
( 2x + 200 ) + ( 6x ) = 360
8x + 200 = 360
8x = 360 - 200
8x = 160
x = 160/8
x = 20
____________________________
Thus :
Angle A = 5(20) - 3 = 97 degrees
Angle B = 3(20) = 60 degrees
Angle D = 20 + 100 = 120 degrees
____________________________
Sum of the interior angles of any four-sides figures are equal 360 degrees ,
Thus :
Angle A+Angle B+Angle C+Angle D = 360
97 + 60 + Angle C + 120 = 360
Angle C + 120 + 157 = 360
Angle C + 277 = 360
Angle C = 360 - 270 - 7
Angle C = 90 - 7
Angle C = 83 degrees