Question

find y, if $overline{ab}$ bisects $angle dac$ and $overline{cb}$ bisects $angle ace$. after you enter your answer press go. y =

Explanation:

Step1: Find $\angle DAC$

Since $\angle DAE = 58^{\circ}$, and $\angle DAC$ and $\angle DAE$ are supplementary (a straight - line angle), $\angle DAC=180 - 58=122^{\circ}$.

Step2: Find $\angle BAC$

Because $\overline{AB}$ bisects $\angle DAC$, then $\angle BAC=\frac{1}{2}\angle DAC$. So $\angle BAC=\frac{1}{2}\times122^{\circ} = 61^{\circ}$.

Step3: Find $\angle ACE$

$\angle ACE$ and $\angle DAE$ are alternate interior angles (assuming $l_1\parallel l_2$), so $\angle ACE = 58^{\circ}$.

Step4: Find $\angle ACB$

Since $\overline{CB}$ bisects $\angle ACE$, then $\angle ACB=\frac{1}{2}\angle ACE$. So $\angle ACB=\frac{1}{2}\times58^{\circ}=29^{\circ}$.

Step5: Find $y$

In $\triangle ABC$, we know that the exterior - angle property states that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, considering $\triangle ABC$ and the exterior angle at $B$, we can also use the fact that in the angle - bisector situation, $y = \angle ACB$. So $y = 29^{\circ}$.

Answer:

$29$