Question

how can you express each of the numbered angles in terms of x? ∠6 and ∠x, ∠8 and ∠x, ∠3 and ∠6, ∠4 and ∠7 ∠6 and ∠x ∠8 and ∠x ∠3 and ∠6 ∠4 and ∠7 how can you express each of the numbered angles in terms of x? ∠6 and ∠x, ∠8 and ∠x, ∠3 and ∠6, ∠4 and ∠7 ∠7 and ∠x ∠7 and ∠2 ∠3 and ∠7 ∠1 and ∠8

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle6$ and the angle with measure $x^{\circ}$ are vertical angles, so $\angle6=x^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle8$ and the angle with measure $x^{\circ}$ are corresponding angles. If the lines are parallel, $\angle8 = x^{\circ}$.

Step3: Identify alternate - interior angles

$\angle3$ and $\angle6$ are alternate - interior angles. If the lines are parallel, $\angle3=\angle6 = x^{\circ}$.

Step4: Identify alternate - interior angles

$\angle4$ and $\angle7$ are alternate - interior angles. If the lines are parallel, $\angle4=\angle7$. Also, $\angle7$ and the angle with measure $x^{\circ}$ are vertical angles, so $\angle7 = x^{\circ}$ and $\angle4=x^{\circ}$.

Answer:

$\angle6=x^{\circ}$, $\angle8 = x^{\circ}$, $\angle3=x^{\circ}$, $\angle4=x^{\circ}$, $\angle7 = x^{\circ}$