In the diagram, two parallel lines are intersected by a transversal. What are the measurements of angles, 1, 2, 4, 5, 6, 7, and 8?

Answer:

1, 6, 8 are each 55 degrees

2, 4, 5, 7 are each 125 degrees.

Step-by-step explanation:

We know 3 things that apply here:

1) When parallel lines are intersected by a transversal, the corresponding angles have the same measure. (the angles in the same position on the parallel line...2 and 4 are equal, 5 and 7 are equal, etc)

2)  Two angles that form a straight line equal 180 degrees

3) Angles that are opposite each other (vertical angles) in this situation are equal. (1 & 6 are equal, 4 & 7 are equal)

So what would be angle #3 is 55 degrees. That means the supplemental angle, #4 is 125 degrees.

Which makes angle 7 125 degrees and angle 8 55 degrees.

And then you apply these rules for angles 1, 2, 5 and 6.

Please let me know if you have any questions.

The measures of the angles are ∠1 = 55°, ∠2 = 125°, ∠4 = 125°, ∠5 = 125°, ∠6 = 55°, ∠7= 125°, and ∠8 = 55°

When a transversal line cut parallel lines, angles are formed such as corresponding angles, alternate angles, vertical angles etc.

Therefore, the measurement of 1, 2, 3, 4, 5, 6, 7 and 8 are as follows;

∠8 = 55°(vertically opposite angles)

∠4 = 180 - 55 = 125° (angle on a straight line)

∠7 = 125° (vertical angles)

∠6 = 55°(alternate angles)

∠2 = 125°(alternat angles)

∠1 = 55°(vertical angles)

∠5 = 125°(vertical angles)

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