Question

m∠1 =
m∠2 =
m∠3 =
m∠4 =
m∠5 =

Explanation:

Step1: Find $m\angle1$

Since $\angle1$ and the $88^{\circ}$ angle are vertical - angles, vertical angles are equal. So $m\angle1 = 88^{\circ}$.

Step2: Find $m\angle3$

$\angle3$ and the $81^{\circ}$ angle are vertical - angles. Vertical angles are equal, so $m\angle3=81^{\circ}$.

Step3: Find $m\angle2$

In the top - triangle, the sum of interior angles of a triangle is $180^{\circ}$. Let the triangle have angles $\angle1$, $\angle2$ and $\angle3$. So $m\angle2=180^{\circ}-m\angle1 - m\angle3$. Substitute $m\angle1 = 88^{\circ}$ and $m\angle3 = 81^{\circ}$ into the formula: $m\angle2=180^{\circ}-88^{\circ}-81^{\circ}=11^{\circ}$.

Step4: Find $m\angle4$

$\angle4$ and the angle adjacent to the $94^{\circ}$ angle (let's call it $\angle x$) are vertical - angles. First, find $\angle x$. Since $\angle x$ and $94^{\circ}$ are supplementary (a straight - line is $180^{\circ}$), $\angle x = 180^{\circ}-94^{\circ}=86^{\circ}$. So $m\angle4 = 86^{\circ}$.

Step5: Find $m\angle5$

In the bottom - triangle, the sum of interior angles of a triangle is $180^{\circ}$. Let the triangle have angles $\angle3$, $\angle4$ and $\angle5$. So $m\angle5=180^{\circ}-m\angle3 - m\angle4$. Substitute $m\angle3 = 81^{\circ}$ and $m\angle4 = 86^{\circ}$ into the formula: $m\angle5=180^{\circ}-81^{\circ}-86^{\circ}=13^{\circ}$.

Answer:

$m\angle1 = 88^{\circ}$
$m\angle2 = 11^{\circ}$
$m\angle3 = 81^{\circ}$
$m\angle4 = 86^{\circ}$
$m\angle5 = 13^{\circ}$