Question

1. draw an example of the alternate interior angles theorem. 78. find $m\angle 1$ in the figure below. $\overleftrightarrow{pq}$ and $\overleftrightarrow{rs}$ are parallel.a $112^\circ$b $102^\circ$c $12^\circ$9. in the figure, $m\angle abc = 126^\circ$. which statement is false?$m\angle gef = 54^\circLXB0\angle hbf$ and $\angle aed$ are alternate interior angles.

Explanation:

For Question 8:

Step1: Identify supplementary angle

The 78° angle and its adjacent angle on line $\overleftrightarrow{PQ}$ are supplementary.
$180^\circ - 78^\circ = 102^\circ$

Step2: Apply parallel lines angle rule

The resulting angle and $\angle 1$ are alternate interior angles, so they are equal.
$m\angle 1 = 102^\circ$

1. $\angle ABC = 126^\circ$, so its supplementary angle on line $AF$ is $180^\circ - 126^\circ = 54^\circ$. Since $BC \parallel ED$, $\angle GEF$ is equal to this supplementary angle, so $m\angle GEF = 54^\circ$ is true.
2. $\angle DEF$ forms a linear pair with the 54° $\angle GEF$, so $m\angle DEF = 180^\circ - 54^\circ = 126^\circ$, not $54^\circ$.
3. $\angle HBF$ and $\angle AED$ are on opposite sides of the transversal $AF$, between the parallel lines $BC$ and $ED$, so they are alternate interior angles, making this statement true.

Answer:

B. $102^\circ$

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For Question 9: