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The ratio of the same side interior angles of two parallel lines is 1:14. find the measures of all eight angles formed by the parallel lines and transversals.

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Answer:

x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees.

Explanation:

The ratio of the same side interior angles of two parallel lines is 1:14, which means that for every one degree of the first angle, the second angle measures 14 degrees. If the first angle is x degrees, then the second angle is 14x degrees.

Since the lines are parallel and the angles are on the same side of the transversal, the alternate interior angles are congruent, so the measure of the third angle is also x degrees, and the measure of the fourth angle is also 14x degrees.

Since the lines are parallel, the alternate exterior angles are also congruent, so the measure of the fifth angle is also x degrees, and the measure of the sixth angle is also 14x degrees.

Finally, the measures of the seventh and eighth angles can be found by adding the measures of the adjacent angles. The seventh angle is adjacent to the third and fifth angles, so its measure is x + x = 2x degrees. The eighth angle is adjacent to the fourth and sixth angles, so its measure is 14x + 14x = 28x degrees.

In summary, the measures of the eight angles formed by the parallel lines and transversal are x degrees, 14x degrees, x degrees, 14x degrees, x degrees, 14x degrees, 2x degrees, and 28x degrees. The value of x can be determined by knowing the measure of one of the angles, or by using other information about the angles or the parallel lines.

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