Parallelograms don’t know how to solve and teacher won’t show me need help

9514 1404 393

Step-by-step explanation:

The marked angles are all "interior" -- between the parallel lines. Ones on the same side of the transversal (t) are called "same-side" or "consecutive" interior angles. Angles 1 and 4, 2 and 3 are pairs of consecutive interior angles.

Angles on opposite sides of the transversal are called "alternate" interior angles. Pairs 1 and 3, and 2 and 4 are pairs of alternate interior angles.

Alternate interior angles are congruent. Consecutive interior angles are supplementary (as are the angles of any linear pair).

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1) Angles ∠1 and ∠3 are congruent.

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2) Using the above fact, we can set the expressions for the angle measures equal to solve for x.

  5x -2 = 2x +55

  5x = 2x +57 . . . . . add 2

  3x = 57 . . . . . . . . . subtract 2x

  x = 19 . . . . . . . . . . divide by 3

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3) Angle 1 is ...

  ∠1 = 5x -2 = 5(19) -2 = 93

Angle 4 is its supplement.

  ∠4 = 180 -∠1 = 180 -93

  ∠4 = 87 . . . degrees

3/4 and -3/4

or

0.75 and -0.75

but there is no solution for

10 times the smaller number added to 6 times the larger number to get 3 as result.

the absolute values of x and y must be equal and with opposite signs (due to their sum being 0).

therefore, 10 times the negative value can never be compensated by 6 times the same but positive value. the sum will always be negative and not positive (and therefore not +3).

it only works with 10 times the larger (positive) number plus 6 times the smaller (negative) value.

Step-by-step explanation:

x + y = 0

10×x + 6×y = 3

=>

x = -y

10×(-y) + 6×y = 3

-10y + 6y = 3

-4y = 3

y = -3/4

=>

x = -y = -(-3/4) = 3/4

control :

10×(3/4) + 6×(-3/4) = 30/4 - 18/4 = 3

12/4 = 3

3 = 3

correct