Answer:
m∠C = 50 degrees
Explanation:
∠CAQ is a straight angle (180) so ∠CAB is supplementary to ∠QAB
∠CAQ = ∠QAB + ∠CAB
180 = 110 + ∠CAB
180 - 110 = ∠CAB
70 = ∠CAB
The total angle measurement in all triangles is 180 degrees, knowing this, we can set up the equation:
180 = ∠CBA + ∠BCA + ∠CAB
180 = 2 + 29x + 24x + 2 + 70
180 = 74 + 53x
180 - 74 = 53x
106 = 53x
2 = x
Knowing x = 2, we can solve for m∠C
24(2) + 2 = ∠C
48 + 2 = ∠C
50 = ∠C