Correct Answer: 90°

Solution :
Given: In $\triangle$ABC, AD$\perp$BC and AD ² = BD × DC.
Applying Pythagoras theorem in $\triangle$ADB and $\triangle$ADC,
AB ² = AD ² + BD ² ____(i)
AC ² = AD ² + DC ² ____(ii)
Adding equation (i) and (ii),
AB ² + AC ² = AD ² + BD ² + AD ² + DC ²
AB ² + AC ² = 2AD ² + BD ² + DC ²
AB ² + AC ² = 2 BD × DC + BD ² + DC ²
AB ² + AC ² = (BD + DC) ²
AB ² + AC ² = BC ²
$\triangle$ABC is a right-angled triangle.
$\angle$BAC = 90°
Hence, the correct answer is 90°.