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 transversal. Sorry! Would appreciate if you give the answer by Tuesday! Thanks

Answers

Answer 1

Answer:

Given that the same-side interiorangles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:

m<1 = 12°

m<2 = 168°

m<3 = 168°

m<4 = 12°

m<5 = 12°

m<6 = 168°

m<7 = 168°

m<8 = 12°

Applying the knowledge of ratio, transversal and parallel lines, we can determine the measures of all 8 angles that are formed when a transversal intersects two parallel lines as shown in the image attached below.

Let < 1 and < 6 be the two same-side interior angles whose measures are in the ratio, 1:14.

Thus:

m<1 : m<6 = 1 : 14

Recall:

Same-side interior angles are always supplementary. That is,

m<1 + m<6 = 180 degrees.

Let's apply ratio to find the measure of <1 and <6.

m<1 = ratio of <1 / sum of ratio x 180

$m \angle 1 = (1)/(1 + 14) * 180\n\nm \angle 1 = (1)/(15) * 180\n\nm \angle 1 = 12^(\circ)$

m<6 = ratio of <6 / sum of ratio x 180

$m \angle 6 = (14)/(1 + 14) * 180\n\nm \angle 6 = (14)/(15) * 180\n\nm \angle 6 = 168^(\circ)$

Since we know the measure of <1 and <6, we can find the measure of others as follows:

m<2 = m<6 = 168° (corresponding angles are congruent)

m<3 = m<6 = 168° (alternate interior angles are congruent)

m<4 = m<1 = 12° (vertical angles are congruent)

m<5 = m<1 = 12° (corresponding angles are congruent)

m<7 = m<6 = 168° (vertical angles are congruent)

m<8 = m<4 = 12° (corresponding angles are congruent)

In conclusion, given that the same-side interiorangles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:

m<1 = 12°

m<2 = 168°

m<3 = 168°

m<4 = 12°

m<5 = 12°

m<6 = 168°

m<7 = 168°

m<8 = 12°

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Answer 2

Answer:

Answer:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.

We know that the sum of interior angles equals 180°.

So, a + b = 180°

a + 14a = 180°

15a = 180°

a = 180/15

a = 12°

At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°

The angle vertically opposite to a is d = a = 12°

The angle vertically opposite to a is b = e = 168°

At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°

the angle vertically opposite to angle b is g = b = 168°

the angle vertically opposite to f is h = 12°

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Answers

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Keywords: rectangle, linear equation

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Answers

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