Question

1. find the value of x. 7. find m∠1 and m∠2. justify each answer by using one of the following angle pairs: alternate interior, alternate exterior, same side interior, corresponding, vertical, or linear pair

Explanation:

Step1: Set up equation for question 6

Since the two angles are same - side interior angles and supplementary (sum to 180°), we have the equation $(x + 109)+(x + 89)=180$.

Step2: Simplify the left - hand side

Combine like terms: $x+x+109 + 89=2x+198$. So, $2x+198 = 180$.

Step3: Solve for x

Subtract 198 from both sides: $2x=180 - 198=-18$. Then divide both sides by 2: $x=\frac{-18}{2}=-9$.

Step4: Analyze angles in question 7

For the 103° angle and ∠1, they are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal. So $m\angle1 = 103^{\circ}$.

Step5: Analyze ∠1 and ∠2

∠1 and ∠2 are a linear - pair. A linear - pair of angles are supplementary (sum to 180°). So $m\angle2=180 - 103 = 77^{\circ}$.

Answer:

For question 6: $x=-9$
For question 7:
$m\angle1 = 103^{\circ}$, Reason: Corresponding angles
$m\angle2 = 77^{\circ}$, Reason: Linear pair