Question

in the figure shown, if ∠1 = 143°. find m∠2, m∠3, and m∠4.
m∠2 = °
m∠3 = °
m∠4 = °

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $m\angle3=m\angle1 = 143^{\circ}$.

Step2: Use linear - pair property

$\angle1$ and $\angle4$ form a linear pair. The sum of angles in a linear pair is $180^{\circ}$. So $m\angle4=180 - m\angle1=180 - 143=37^{\circ}$.

Step3: Use vertical - angle property again

$\angle2$ and $\angle4$ are vertical angles. So $m\angle2=m\angle4 = 37^{\circ}$.

Answer:

$m\angle2 = 37^{\circ}$
$m\angle3 = 143^{\circ}$
$m\angle4 = 37^{\circ}$