Question

find the measures of the missing angles. m∠1 = m∠2 = m∠3 = m∠4 =

Explanation:

Step1: Vertical - angle property

Vertical angles are equal. $\angle1$ and the $47^{\circ}$ angle are vertical angles, so $m\angle1 = 47^{\circ}$.

Step2: Complementary - angle property

$\angle1$ and $\angle2$ are complementary (form a right - angle, $90^{\circ}$). So $m\angle2=90^{\circ}-m\angle1$. Substituting $m\angle1 = 47^{\circ}$, we get $m\angle2 = 90^{\circ}-47^{\circ}=43^{\circ}$.

Step3: Vertical - angle property

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3 = m\angle2=43^{\circ}$.

Step4: Vertical - angle property

$\angle3$ and $\angle4$ are vertical angles. So $m\angle4 = m\angle3 = 43^{\circ}$.

Answer:

$m\angle1 = 47^{\circ}$, $m\angle2 = 43^{\circ}$, $m\angle3 = 43^{\circ}$, $m\angle4 = 43^{\circ}$