Question

1. find the measure of each missing angle. m∠1 = ______ m∠2 = ____ m∠3 = ____ m∠4 = ____ m∠5 = ______

Explanation:

Step1: Use angle - sum property of a right - triangle for the small right - triangle

In the small right - triangle, one angle is $90^{\circ}$ and let's assume we first find $\angle1$. The sum of angles in a triangle is $180^{\circ}$. So for the small right - triangle with one non - right angle given as $35^{\circ}$, we have $m\angle1 + 35^{\circ}+90^{\circ}=180^{\circ}$. Then $m\angle1=180^{\circ}-(90^{\circ} + 35^{\circ})=55^{\circ}$.

Step2: Use vertical angles property

$\angle1$ and $\angle2$ are vertical angles. Vertical angles are equal. So $m\angle2 = m\angle1=55^{\circ}$.

Step3: Use angle - sum property of a right - triangle for the large right - triangle

In the large right - triangle, one angle is $90^{\circ}$ and $\angle2 = 55^{\circ}$. Then $m\angle3=180^{\circ}-(90^{\circ}+55^{\circ}) = 35^{\circ}$.

Step4: Use vertical angles property

$\angle3$ and $\angle4$ are vertical angles. So $m\angle4=m\angle3 = 35^{\circ}$.

Step5: Use angle - sum property of a right - triangle for the small right - triangle again

In the small right - triangle with right angle and $\angle4 = 35^{\circ}$, $m\angle5=180^{\circ}-(90^{\circ}+35^{\circ})=55^{\circ}$.

Answer:

$m\angle1 = 55^{\circ}$
$m\angle2 = 55^{\circ}$
$m\angle3 = 35^{\circ}$
$m\angle4 = 35^{\circ}$
$m\angle5 = 55^{\circ}$