Question

m∠1 =

m∠2 =

m∠3 =

Explanation:

Step1: Find angle 1

Use the angle - sum property of a triangle. The sum of angles in a triangle is 180°. In the right - hand triangle, if two angles are 61° and 68°, then $m\angle1=180-(61 + 68)$.
$m\angle1=180 - 129=51^{\circ}$

Step2: Find angle 2

Angle 2 and the non - right angle adjacent to it in the left - hand triangle are vertical angles with the angles in the right - hand triangle. Since vertical angles are equal, and we know that the non - right angle adjacent to angle 2 is equal to the non - right angle in the right - hand triangle corresponding to it. Also, note that angle 2 and the 61° angle are vertical angles. So $m\angle2 = 61^{\circ}$

Step3: Find angle 3

In the left - hand triangle, we know one angle is 90° (right angle) and angle 2 is 61°. Using the angle - sum property of a triangle ($180^{\circ}$ for the sum of interior angles of a triangle), we have $m\angle3=180-(90 + 61)$.
$m\angle3=180 - 151 = 29^{\circ}$

Answer:

$m\angle1 = 51^{\circ}$
$m\angle2 = 61^{\circ}$
$m\angle3 = 29^{\circ}$