Question

use the diagram and the given angle measure to find the other three. m∠1 = 143°. m∠2 = °. m∠3 = °. m∠4 = °.

Explanation:

Step1: Identify vertical and supplementary angles

Angles 1 and 3 are vertical angles, angles 1 and 2 are supplementary, and angles 2 and 4 are vertical angles.

Step2: Find angle 3

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

Step3: Find angle 2

Supplementary angles add up to $180^{\circ}$. Since $\angle1$ and $\angle2$ are supplementary, $m\angle2 = 180^{\circ}-m\angle1$. So $m\angle2=180 - 143=37^{\circ}$.

Step4: Find angle 4

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

Answer:

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