Question

Find the measure of angle DCA if D is the incenter of the triangle ABC.
http://curriculum.kcdistancelearning.com/courses/GEOMx-HS-A09/a/assessments/T-TrianglesUnitExam/Geometry_Unit4_Exam_25q.gif

Answer 1

let the measure of DCA is x, so DCB also x (remember that bisector always divides an angle in triangle be same 2 parts), and we knowed that the sum all interior angles in a triangle is 180 degrees, therefore we can represent it be :
2*32 + 2*37 + 2x = 180, solve for x

Answer 2

so the answer be DCA = 21

Answer 3

2*32 + 2*37 + 2x = 180
64 + 74 + 2x = 180
138 + 2x = 180
2x = 180-138
2x = 42
x = 42/2 = 21
u are right