Question

Question was provided via image upload.

Explanation:

Step1: Calculate $m\angle3$ (supplementary angle)

$\angle3 + 84^\circ = 180^\circ$
$m\angle3 = 180^\circ - 84^\circ = 96^\circ$

Step2: Calculate $m\angle1$ (triangle sum)

$m\angle1 + 66^\circ + 84^\circ = 180^\circ$
$m\angle1 = 180^\circ - 66^\circ - 84^\circ = 30^\circ$

Step3: Calculate $m\angle2$ (triangle sum)

$m\angle2 + 43^\circ + 96^\circ = 180^\circ$
$m\angle2 = 180^\circ - 43^\circ - 96^\circ = 41^\circ$

Answer:

$m\angle1 = 30^\circ$
$m\angle2 = 41^\circ$
$m\angle3 = 96^\circ$