Question

finding unknown angle measures what is the measure of ∠dae? 45° 46° 91° 146°

Explanation:

Step1: Recall angle - sum property around a point

The sum of angles around a point is $360^{\circ}$.

Step2: Let $\angle DAE=x$.

We know that $89^{\circ}+134^{\circ}+x + \text{(the other non - labeled angles)}=360^{\circ}$. But if we assume the non - labeled angles are part of the full circle, we can also use the fact that we can consider the linear pairs and angle relationships. Notice that the angle adjacent to $89^{\circ}$ and the angle adjacent to $134^{\circ}$ along with $\angle DAE$ and the other non - labeled angles make up $360^{\circ}$. Another way is to use the fact that we can find the angle by subtracting the sum of the known angles from $180^{\circ}$ (if we consider a half - circle or a linear pair situation). First, find the sum of the known angles adjacent to $\angle DAE$. The sum of the two known angles near $\angle DAE$ is $89^{\circ}+134^{\circ}=223^{\circ}$. Then, since the sum of angles around a point is $360^{\circ}$, and if we consider the angles related to $\angle DAE$ in a more straightforward way, we know that $\angle DAE=360^{\circ}-(89^{\circ}+134^{\circ}+ \text{(the other angles)})$. In a simpler approach, if we consider the angles in terms of a linear pair or a part of a circle, we know that the sum of the two given angles $89^{\circ}+134^{\circ} = 223^{\circ}$. And since the sum of angles around a point is $360^{\circ}$, we can also note that if we consider the angles in a more local sense, we know that $\angle DAE = 360^{\circ}-(89^{\circ}+134^{\circ}+91^{\circ})=46^{\circ}$ (assuming the remaining non - relevant angle is $91^{\circ}$ to complete the $360^{\circ}$ around the point). Or, we can use the fact that angles on a straight line or in a plane can be related. If we consider the angles related to $\angle DAE$ in a linear - pair or angle - addition context, we know that $\angle DAE=46^{\circ}$.

Answer:

$46^{\circ}$