Question

in the figure below, $m\angle 3 = 144^{\circ}$. find $m\angle 1$, $m\angle 2$, and $m\angle 4$.
$m\angle 1 = \square^{\circ}$
$m\angle 2 = \square^{\circ}$
$m\angle 4 = \square^{\circ}$

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle2\) and \(\angle3\) are supplementary (they form a linear pair), \(m\angle2 + m\angle3=180^{\circ}\).
Given \(m\angle3 = 144^{\circ}\), then \(m\angle2=180^{\circ}-144^{\circ}=36^{\circ}\).

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle3\) are vertical angles. Vertical angles are equal. So \(m\angle1 = m\angle3=144^{\circ}\).

Step3: Find \(m\angle4\)

\(\angle4\) and \(\angle2\) are vertical angles. Vertical angles are equal. So \(m\angle4 = m\angle2 = 36^{\circ}\).

Answer:

\(m\angle1 = 144^{\circ}\)
\(m\angle2 = 36^{\circ}\)
\(m\angle4 = 36^{\circ}\)