Question

in the figure below, m∠3 = 43°. find m∠1, m∠2, and m∠4.
figure of two intersecting lines creating angles 1, 2, 3, 4 with angle 3 labeled 43° and a box to fill m∠1, m∠2, m∠4 with degree symbols

Explanation:

Step1: Identify vertical angles

$\angle1$ and $\angle3$ are vertical angles, so $m\angle1 = m\angle3 = 43^\circ$.

Step2: Calculate $\angle2$ (supplementary to $\angle3$)

$\angle2 + \angle3 = 180^\circ$, so $m\angle2 = 180 - 43 = 137^\circ$.

Step3: Identify vertical angles for $\angle4$

$\angle4$ and $\angle2$ are vertical angles, so $m\angle4 = m\angle2 = 137^\circ$.

Answer:

$m\angle1 = 43^\circ$, $m\angle2 = 137^\circ$, $m\angle4 = 137^\circ$