Answer:
x=11
∠DMC=39
∠MAD=66
∠ADM=36
∠ADC=18
Step-by-step explanation:
Since c is the incenter, CA, CM and CD bisect ∠DAM, ∠AMD and ∠ADM respectively. Therefore, ∠CAD=∠CAM, ∠AMC= ∠DMC, and ∠ADC=∠MDC.
X
∠AMC= ∠DMC
3x+6=8x-49
5x=55
x=11
∠DMC
∠DMC=8x-49=8(11)-49=88-49=39
∠MAD
∠CAD=∠CAM
∠MAD=∠CAD+∠CAM.
∠MAD=33+33=66
∠ADM
∠DMA=2(∠DMC)=2(39)=78
Angles in a triangle add to 180:
∠MAD+∠ADM+∠DMA=180
66+∠ADM+78=180
∠ADM=180-144=36
∠ADC
∠ADM=2(∠ADC)
∠ADC=36/2=18
