Question

if bc ≅ be and m∠bdc = 38°, what is m∠cde? m∠cde = °

Explanation:

Step1: Recall congruent - triangle property

Since $\overline{BC}\cong\overline{BE}$ and $\angle BCD=\angle BED = 90^{\circ}$ and $\overline{BD}=\overline{BD}$ (common side), by the Hypotenuse - Leg (HL) congruence criterion, $\triangle BCD\cong\triangle BED$.

Step2: Use corresponding - angles property

If $\triangle BCD\cong\triangle BED$, then $\angle BDC=\angle BDE$. Given that $m\angle BDC = 38^{\circ}$, so $m\angle BDE=38^{\circ}$.

Step3: Calculate $\angle CDE$

$\angle CDE=\angle BDC+\angle BDE$. Substituting the values, we get $\angle CDE = 38^{\circ}+38^{\circ}=76^{\circ}$.

Answer:

$76$