Question

1. m∠1 = __ m∠2 = m∠3 = __ 75° 41° 54°

Explanation:

Step1: Find angle 1

The sum of angles in a triangle is 180°. In the top - triangle, we have two known angles 75° and 41°. So, $m\angle1=180-(75 + 41)$.
$m\angle1=180 - 116=64^{\circ}$

Step2: Find angle 2

In the right - angled triangle with angle 54°, since it's a right - triangle, one angle is 90°. Using the angle - sum property of a triangle ($180^{\circ}$), we have $m\angle2=180-(90 + 54)$.
$m\angle2=180 - 144 = 36^{\circ}$

Step3: Find angle 3

The angle adjacent to the right - angle in the right - angled triangle and angle 3 are vertical angles. First, note that the non - right angles in the right - angled triangle are 36° and 54°. Angle 3 and the 54° angle are complementary (because of the straight line formed with the right - angle). So $m\angle3 = 54^{\circ}$

Answer:

$m\angle1 = 64^{\circ}$, $m\angle2=36^{\circ}$, $m\angle3 = 54^{\circ}$