3. Let $ABC$ be a right isosceles triangle, $\mathrm{m}(\widehat{BAC})=90^{\circ}$. At point $C$, a perpendicular is raised to the plane $(ABC)$, on which point $D$ is considered such that $\mathrm{m}(\widehat{DBC})=45^{\circ}$. Determine the measure of the angle $\widehat{ABD}$.
3. From the theorem of the three perpendiculars, it follows that $A D \perp A B$. $2 p$

Denoting $A B=a$ it follows that $B C=a \sqrt{2}, D C=B C=a \sqrt{2}$, and in the right triangle $C A D$, $A D=a \sqrt{3}$ $.3 p$

In the right triangle $A B D$ it follows that $\operatorname{tg} \widehat{A B D}=\frac{a \sqrt{3}}{a}=\sqrt{3}$, hence $\mathrm{m}(\overline{A B D})=60^{\circ}$ . $.2 p$

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