Question

5.
$m\angle1 = \underline{\quad}$
$m\angle2 = \underline{\quad}$
$m\angle3 = \underline{\quad}$

Explanation:

Step1: Calculate $m\angle1$

In the right triangle, angles sum to $180^\circ$.
$$m\angle1 = 180^\circ - 90^\circ - 43^\circ = 47^\circ$$

Step2: Calculate $m\angle2$

$\angle2$ is supplementary to $43^\circ$.
$$m\angle2 = 180^\circ - 43^\circ = 137^\circ$$

Step3: Calculate $m\angle3$

In the small triangle, angles sum to $180^\circ$.
$$m\angle3 = 180^\circ - 137^\circ - 12^\circ = 31^\circ$$

Answer:

$m\angle1 = 47^\circ$
$m\angle2 = 137^\circ$
$m\angle3 = 31^\circ$