Question

What is the measure of c ?

Answer 1

Judging by the model I noticed that < D for ^ABCD is 32, so I'd assume that the <D for ^CBD is 16. 

The next step is to realize that all angles in a triangle add up to 180, so to find <c you need to solve this equation 180= <B + <D + <C.
 
We already have <D which is 16, and <B is a right angle, so 90. The equation now is 180= 90 + 16 + <C. which simplified is 180= 106 + <C.

I then subtract 106 from both sides to get <C = 74.

Hope this helped out! <3

Answer 2

58°
The triangles are congruent through SSS (side-side-side), so all the angles and sides are the same.
m∠CDB = 32 °
m∠DBC = 90 °
Triangle equals 180 degrees so....
180 - 32 - 90 = m∠C
58 = m∠C