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lubasha [3.4K]
2 years ago
3

Using the diagram below classify the angle pairs as corresponding, alternate interior angles, alternate exterior angles, consecu

tive interior or none.

Mathematics
1 answer:
QveST [7]2 years ago
5 0

Answer:

The corresponding angles in pairs are;

∠1 and ∠5, ∠2 and ∠6, ∠9 and ∠13, ∠10 and ∠14,

∠3 and ∠7, ∠4 and ∠8, ∠11 and ∠15, ∠12 and ∠16

∠1 and ∠3, ∠2 and ∠4, ∠9 and ∠11, ∠10 and ∠12

∠7 and ∠5, ∠8 and ∠6, ∠15 and ∠13, ∠16 and ∠14

The alternate interior angles are;

∠9 and ∠4, ∠10 and ∠3, ∠8 and ∠13, ∠7 and ∠14

∠2 and ∠13, ∠10 and ∠5, ∠4 and ∠15, ∠7 and ∠12

The alternate exterior angles are;

∠1 and ∠12, ∠2 and ∠11, ∠5 and ∠16, ∠6 and ∠15

∠1 and ∠14, ∠9 and ∠6, ∠3 and ∠16, ∠11 and ∠8

Consecutive interior angles

∠9 and ∠3, ∠10 and ∠4, ∠13 and ∠7, ∠14 and ∠8

∠2 and ∠5, ∠10 and ∠13, ∠4 and ∠7, ∠12 and ∠15

None

Some of the angles without specific relations are;

∠1 and ∠4, ∠2 and ∠3, ∠5 and ∠8, ∠6 and ∠7, ∠9 and ∠12, ∠10 and ∠11, ∠13 and ∠16, ∠14 and ∠15, ∠6 and ∠12, ∠5 and ∠11, ∠1 and ∠16, ∠2 and ∠15, ∠1 and ∠8, ∠2 and ∠12, ∠9 and ∠7, ∠10 and ∠8

Step-by-step explanation:

Corresponding angles are angles on the same side of two lines that are crossed by a given transversal

Alternate interior angles are angles on the inner but opposite sides of two lines crossed by a transversal

Alternate exterior angles are angles on the outer but opposite sides of two lines crossed by a transversal

Consecutive interior angles are angles that are next to each other on the same side of the transversal and in between the two lines.

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$ 454.86 : $33.25

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Alex bought the new easy chair for $ 399 .

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Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

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⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
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We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
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Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

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So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:

   -3 + ix²y 
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The vertical or y intercepts will be zeroes of the following factors.

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