In $\triangle$ ABC, AD is perpendicular to BC and AE is the bisector of $\angle$BAC . If $\angle ABC = 58^{\circ}$ and $\angle ACB = 34^{\circ}$, then find the measure of $\angle$DAE.

12°

AD is perpendicular to BC and AE is the bisector of \(\angle\)BAC, then

\(\angle\)DAE = (\(\angle\)B - \(\angle\)C)/2

⇒ (\({58}^\circ\) - \({34}^\circ\))/2

⇒ \({24}^\circ\)/2 = \({12}^\circ\)

Therefore, \(\angle\)DAE is \({12}^\circ\)