Use the figure to answer the question.

An illustration shows a right inclined transversal passing through two parallel lines labeled upper M and upper N. Four angles are formed at the intersections of the transversal with upper M and upper N.

If M
and N
are parallel and angle 1 is 135°
, what is the sum of angle 6 and angle 8?

3 answers

To determine the sum of angle 6 and angle 8, we need to analyze their relationships given that M and N are parallel lines and angle 1 is 135.

In this scenario, we can use the properties of angles formed by a transversal intersecting parallel lines:

  1. Corresponding Angles: Corresponding angles are equal.
  2. Alternate Interior Angles: Alternate interior angles are equal.
  3. Consecutive Interior Angles (Same-Side Interior Angles): These angles are supplementary (they add up to 180).

If we designate the angles as follows based on their positions:

  • Angle 1 is given as 135.

Here's the relationship between the angles:

  • Angle 1 (which is 135) and angle 8 are on the same side of the transversal and are supplementary.
  • Therefore, angle 1 and angle 8 satisfy the relationship: angle 1+angle 8=180 Substituting 135 for angle 1: 135+angle 8=180 Solving for angle 8 gives: angle 8=180135=45

Since angle 6 is vertically opposite to angle 8 (because of the transversal crossings), then:

  • Angle 6 is equal to angle 8: angle 6=45

Now, we can find the sum of angle 6 and angle 8: Sum of angle 6 and angle 8=angle 6+angle 8=45+45=90.

Thus, the sum of angle 6 and angle 8 is 90.

I apologize for the confusion in my previous response. Let's reanalyze the problem step-by-step given that angle 1 is 135.

Given:

  • Transversal intersects two parallel lines M and N.
  • Angle 1 is 135.

Understand the angles:

  1. Angle 1 is one of the angles formed by the transversal intersecting line M.
  2. Since lines M and N are parallel and angle 1 is at the intersection of the transversal with line M, we know:
    • Angle 2 (which is vertically opposite to angle 1) is also 135.
    • Angle 3 (corresponding angle to angle 1 at line N) is also 135.
    • Angle 4 (the angle that is supplementary to angle 1) gives: Angle 4=180135=45.

Next, let’s place the angles:

  • If angle 1 is 135:
    • Angle 2 (vertically opposite to angle 1) is 135.
    • Angle 3 (corresponding to angle 1 at line N) is 135.
    • Angle 4=45 (same side interior angle).

Relating with angle 6 and angle 8:

  • Angle 8 (which is on the same side as angle 1, and interior to line N) is supplementary to angle 3:

    • Therefore, Angle 8=180Angle 3=180135=45.
  • Angle 6, which is vertically opposite to angle 4 (and therefore also equals angle 4), is again:

    • Angle 6=45.

Final Calculation:

Now, the sum of angle 6 and angle 8 is: Angle 6+Angle 8=45+45=90.

So, the correct answer is still 90. If I've misunderstood any part of your setup or the diagram, please provide further clarification!

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