Answer
$\angle1=120^{\circ}, \angle2=60^{\circ}, and \angle3=30^{\circ}$
Work Step by Step
This is an equilateral triangle. Let's remember that the measure in each interior angle its $60^{\circ}$
The radius is atually the bisector of the interior angle.So, $\angle3=30^{\circ}$
The sum of the angles of any triangle is $180^{\circ}$ Using this property applied to this we get
$\angle2+\angle3+90^{\circ}= 180^{\circ}$
$\angle2=180^{\circ}-\angle3-90^{\circ}$
$\angle2=60^{\circ}$
Using the same property we got
$\angle1+30^{\circ}=180^{\circ}$
$\angle1=180^{\circ}-30^{\circ}-30^{\circ}$
$\angle1=180^{\circ}-60^{\circ}$
$\angle1=120^{\circ}$
