Question

1. find each angle measure.

$m\angle1 = ___$
$m\angle2 = ___$
$m\angle3 = 38^{circ}$
$m\angle4 = 84^{circ}$
$m\angle5 = ___$
$m\angle6 = ___$

Explanation:

Step1: Find angle 1

In the right - triangle on the right, since one angle is 90° and another is given as 52°, and the sum of angles in a triangle is 180°. So, $m\angle1=180^{\circ}-90^{\circ}-52^{\circ}=38^{\circ}$.

Step2: Find angle 2

Angle 1 and angle 2 are vertical angles. Vertical angles are equal. So, $m\angle2 = m\angle1=38^{\circ}$.

Step3: Find angle 5

In the right - triangle on the right, $m\angle5 = 90^{\circ}-m\angle1=90^{\circ}-38^{\circ}=52^{\circ}$.

Step4: Find angle 6

In the right - triangle on the left, one angle is 90° and another is 52°. So, $m\angle6=90^{\circ}-52^{\circ}=38^{\circ}$.

Answer:

$m\angle1 = 38^{\circ}$
$m\angle2 = 38^{\circ}$
$m\angle5 = 52^{\circ}$
$m\angle6 = 38^{\circ}$