Question

given that $m \parallel \overleftrightarrow{yz}$. why is the measure of the interior angles of $\triangle xyz$ $180^\circ$? drag and drop the answers into the boxes to correctly complete the statement. $\angle 1$, $\angle 3$, and $\angle 2$ form a straight angle. the measure of a straight angle is \boxed{} so $m\angle 1 + m\angle 3 + m\angle 2 = \boxed{}$. $\angle 1$ and $\angle 5$ are \boxed{} angles for transversal \boxed{} since $m \parallel \overleftrightarrow{yz}$, \boxed{} angles are \boxed{}. so, $\angle 1$ and $\angle 5$ are

Explanation:

Step1: Define straight angle measure

A straight angle measures $180^\circ$.

Step2: Sum of angles on straight line

Since $\angle1, \angle3, \angle2$ form a straight angle, $m\angle1 + m\angle3 + m\angle2 = 180^\circ$.

Step3: Identify angle pair type

$\angle1$ and $\angle5$ are alternate interior angles.

Step4: Identify the transversal

The transversal creating these angles is $\overleftrightarrow{XY}$.

Step5: Apply parallel lines theorem

For parallel lines, alternate interior angles are congruent.

Step6: State congruence of the angles

So, $\angle1$ and $\angle5$ are congruent.

Answer:

1. $180^\circ$
2. $180^\circ$
3. alternate interior
4. $\overleftrightarrow{XY}$
5. Alternate interior
6. congruent