Question

1. 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 no relation ∠4 and ∠7

Explanation:

Step1: Identify angle - relationship for ∠6 and ∠x

∠6 and ∠x are corresponding angles. If the lines are parallel, ∠6 = x.

Step2: Identify angle - relationship for ∠8 and ∠x

∠8 and ∠x are alternate - exterior angles. If the lines are parallel, ∠8 = x.

Step3: Identify angle - relationship for ∠3 and ∠6

∠3 and ∠6 are same - side interior angles. If the lines are parallel, ∠3+∠6 = 180°, so ∠3 = 180 - x (since ∠6 = x).

Step4: Identify angle - relationship for ∠4 and ∠7

∠4 and ∠7 are alternate - interior angles. If the lines are parallel, ∠4 = ∠7. Since ∠7=180 - x (linear pair with ∠6 which is x), ∠4 = 180 - x.

Answer:

∠6 = x; ∠8 = x; ∠3 = 180 - x; ∠4 = 180 - x