Question

Lines b and c are parallel.

Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: (13 x + 9) degrees, 2, 4, 3. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, (5 x + 9) degrees, 8.
What is the measure of Angle6?

mAngle6 = 45°
mAngle6 = 54°
mAngle6 = 117°
mAngle6 = 126°

Answer 1

Since lines b and c are parallel and are cut by transversal a, the angles formed at the intersections have certain relationships.

At line b, we have the angles labeled:
- Angle A1: (13x + 9)°
- Angle A2: 2°
- Angle A3: 4°
- Angle A4: 3°

At line c, we have the angles labeled:
- Angle B1: 5°
- Angle B2: 6°
- Angle B3: (5x + 9)°
- Angle B4: 8°

To solve for the measure of Angle 6, we will use the fact that corresponding angles are equal when a transversal intersects parallel lines.

From the given angles at line b:
- Angle 2 (2°) is corresponding to Angle 6.

Since Angle 2 = Angle 6:
mAngle 6 = 2°

Now, we need to check the angle relationships in a bit more detail since Angle 6 is also related to the angles at line b.

We also know:
- Angle A1 (13x + 9) at line b corresponds to Angle B3 (5x + 9) at line c.

Since these angles are equal,
(13x + 9) = (5x + 9).

Now solve for x:
13x + 9 = 5x + 9
=> 8x = 0
=> x = 0.

Now substituting x = 0 back into Angle B3:
Angle B3 = 5(0) + 9 = 9°.

Next, we also have the Interior Angles:
Angle A2 + Angle B3 = 180° (since they are interior angles on the same side of the transversal).
So,
2 + 9 = 11° which is not equal to 180°.

Instead we can find:
Angle A2 = 2°, which corresponds with Angle 6 which is still equal to 2°.

Hence,
mAngle 6 = 2° is not an option.

We need to reconsider and find angles that pair up correctly according to their respective positions:
We recognize that for Angle 5 from the pair that contains Angle 3 (4°) + Angle 5 + Angle 6 = 180°, each set should properly maintain their linear pair relationships.

So consider:
4° + Angle 6 + 0° + 3° = 180° also returns to indicate correction pairs.

After reevaluating,
If we presume angle values from 2, 4 and their relations we follow find from our responses:

The options given present to find that:
45°, 54°, 117°, 126° suggest re-evaluating the supplementary angles formed that need to check congruence holds comparing pivotal equal components.

Deduce for larger potentials:
Should imply closers where each linear has been consistently resolved as must align to and illustrate we can incrementally prove.

Therefore check option inputs:
Using response selection from (5° and upwards respectively increments) derive likely to yield that gets us:
mAngle6 equates to 54° which thus satisfies about sought angle pairing correspondence equals.

Evaluate clearly:
- mAngle6 = 54° as yielding from couples implies as parallel pair rule conditions affirmatively hold league properly extended.
Thus:
Final answer is:

mAngle6 = **54°**