To determine the sum of angle 6 and angle 8, we need to analyze their relationships given that
In this scenario, we can use the properties of angles formed by a transversal intersecting parallel lines:
- Corresponding Angles: Corresponding angles are equal.
- Alternate Interior Angles: Alternate interior angles are equal.
- Consecutive Interior Angles (Same-Side Interior Angles): These angles are supplementary (they add up to
).
If we designate the angles as follows based on their positions:
- Angle 1 is given as
.
Here's the relationship between the angles:
- Angle 1 (which is
) and angle 8 are on the same side of the transversal and are supplementary. - Therefore, angle 1 and angle 8 satisfy the relationship:
Substituting for angle 1: Solving for angle 8 gives:
Since angle 6 is vertically opposite to angle 8 (because of the transversal crossings), then:
- Angle 6 is equal to angle 8:
Now, we can find the sum of angle 6 and angle 8:
Thus, the sum of angle 6 and angle 8 is