Question

find the shortest side of $\triangle bcd$.

Explanation:

Step1: Find ∠DBC

∠DBC = 180° - 125° = 55°

Step2: Calculate ∠C

∠C = 180° - ∠D - ∠DBC = 180° - 64° - 55° = 61°

Step3: Compare all angles

∠DBC=55°, ∠C=61°, ∠D=64°
The smallest angle is ∠DBC.

Step4: Match side to smallest angle

In a triangle, the shortest side is opposite the smallest angle. ∠DBC is opposite side DC.

Answer:

The shortest side of $\triangle BCD$ is $\overline{DC}$ (or side $DC$)