Question

in the figure below, m∠4 = 139°. find m∠1, m∠2, and m∠3.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles. So $m\angle1 = m\angle4$. Since $m\angle4 = 139^{\circ}$, then $m\angle1=139^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle1 + m\angle2=180^{\circ}$. Substitute $m\angle1 = 139^{\circ}$ into the equation: $139^{\circ}+m\angle2 = 180^{\circ}$, then $m\angle2=180^{\circ}- 139^{\circ}=41^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3 = m\angle2$. Thus $m\angle3 = 41^{\circ}$.

Answer:

$m\angle1 = 139^{\circ}$, $m\angle2 = 41^{\circ}$, $m\angle3 = 41^{\circ}$