Question

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: Set up the equation

Let $\angle DAE=x$. We know that $89^{\circ}+134^{\circ}+x = 360^{\circ}- 180^{\circ}$ (since the non - mentioned angles also form a straight - line pair). Simplifying, we have $89^{\circ}+134^{\circ}+x=180^{\circ}$.

Step3: Solve for $x$

First, add $89^{\circ}$ and $134^{\circ}$: $89 + 134=223^{\circ}$. Then, $x=180^{\circ}-223^{\circ}+360^{\circ}$. Another way is to use the fact that the sum of the three given non - overlapping angles around point $A$ is $360^{\circ}$. So $x = 360-(89 + 134+180)$. $89+134 = 223$, and $360-(223 + 180)=360 - 403+180 = 46^{\circ}$.

Answer:

$46^{\circ}$