Answer:
m< CDF = 58°
Explanation:
Key skills needed: Congruent Triangles
1) We can use Triangle Congruence Rules to prove that Triangle EDF and Triangle CDF are congruent triangles.
2) Since both triangles have 1 right angle, they are both triangle triangles.
3) Both triangles share the same hypotenuse (DF)
Also, it gives us EF is 36, and FC is 36 --> This means that EF ≅ FC
Since both are Right Triangles, we can use Right Triangle HL Congruence to prove it
HL means Hypotenuse-Leg
This rule can only be applied to right angle triangles. In order to use this rule, a hypotenuse and a leg of the triangles need to proven congruent.
4) Since ΔEDF ≅ ΔCDF with Right triangle HL, we can say that < CDF is congruent to < EDF. These are corresponding parts of the triangle.
--> To say that < CDF is congruent to < EDF, we can use the theorem:
If Δs are ≅, then all corresponding parts are ≅.
5) Therefore, <CDF ≅ <EDF (which means the measures of the angles are the same value)
Since <EDF is 58°, <CDF would also be 58°
Hope you understood and have a nice day!! :D