Question

in the figure below, m∠4 = 43°. find m∠1, m∠2, and m∠3.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles.
$m\angle1 = m\angle4$

Step2: Determine $m\angle1$ value

Since $m\angle4 = 43^{\circ}$, then $m\angle1=43^{\circ}$

Step3: Use linear - pair property

$\angle1$ and $\angle2$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle1 + m\angle2=180^{\circ}$

Step4: Calculate $m\angle2$

$m\angle2 = 180^{\circ}-m\angle1=180 - 43=137^{\circ}$

Step5: Use vertical - angle property again

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3 = m\angle2$

Step6: Determine $m\angle3$ value

$m\angle3 = 137^{\circ}$

Answer:

$m\angle1 = 43^{\circ}$
$m\angle2 = 137^{\circ}$
$m\angle3 = 137^{\circ}$