Question

1. given $overline{ab}paralleloverline{cd}$, prove that $mangle1 + mangle2 + mangle3=180$.

Explanation:

Step1: Use alternate - interior angles

Since $\overline{AB}\parallel\overline{CD}$, $\angle2$ and $\angle4$ are alternate - interior angles. So, $m\angle2 = m\angle4$.

Step2: Consider the straight - line angle

$\angle1$, $\angle3$, and $\angle4$ form a straight - line. The sum of angles on a straight - line is $180^{\circ}$. So, $m\angle1 + m\angle3+m\angle4=180^{\circ}$.

Step3: Substitute $\angle4$ with $\angle2$

Substitute $m\angle4$ with $m\angle2$ in the equation $m\angle1 + m\angle3+m\angle4=180^{\circ}$. We get $m\angle1 + m\angle2 + m\angle3=180^{\circ}$.

Answer:

The proof is completed as shown above, and $m\angle1 + m\angle2 + m\angle3 = 180^{\circ}$.