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.
Answer & explanation
Correct answer: option 1
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 \({12}^\circ\)