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umka21 [38]
3 years ago
14

Find the value of x for which ABCD must be a parallelogram.

Mathematics
1 answer:
Musya8 [376]3 years ago
5 0

The value of x is 13°.

Solution:

Given ABCD is a parallelogram.

⇒ AD || BC and AC is a transversal line.

<u>Property of parallel lines:</u>

<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal.</em>

∠DAC = ∠CAB

(4x - 1)° = (x + 38)°

4x° - 1° = x° + 38°

Add 1° on both sides.

4x° - 1° + 1° = x° + 38° + 1°

4x° = x° + 39°

Subtract x° from both sides.

4x° - x° = x° + 39° - x°

3x° = 39°

Divide by 3° on both sides.

x = 13°

The value of x is 13°.

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Answer:y= -4

Step-by-step explanation:

1 Solve for xx in 7x-4y=-127x−4y=−12.

x=\frac{4(y-3)}{7}

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​

2 Substitute x=\frac{4(y-3)}{7}x=

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\frac{36(y-3)}{7}-4y=-20

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36(y−3)

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3 Solve for yy in \frac{36(y-3)}{7}-4y=-20

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y=-4

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4 Substitute y=-4y=−4 into x=\frac{4(y-3)}{7}x=

7

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3 years ago
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stepladder [879]

Answer:

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Step-by-step explanation:

Step 1: Write equation

75 - 3.5x - 4x = 4x + 6

Step 2: Solve for <em>x</em>

  1. Combine like terms: 75 - 7.5x = 4x + 6
  2. Add 7.5x on both sides: 75 = 11.5x + 6
  3. Subtract 6 on both sides: 69 = 11.5x
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<em>Plug in x to verify it's a solution.</em>

75 - 3.5(6) - 4(6) = 4(6) + 6

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