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3 years ago

I need help with this problem plz

Mathematics

1 answer:

VladimirAG [237]3 years ago

5 0

Answer:

x = 18

Step-by-step explanation:

1. Let's solve for x, using the supplementary angles theorem, this way:

∠ C = 180 - 7x + 2 because they are supplementary angles. And these angles add up to 180 degrees.

∠ D = 180 - 9x + 31 because they are supplementary angles. And these angles add up to 180 degrees.

∠ E = 180 - 4x - 33 because they are supplementary angles. And these angles add up to 180 degrees.

Now, let's recall that the interior angles of a triangle add up to 180 degrees. Thus:

∠ C + ∠ D + ∠ E = 180 °

Replacing with the real values for solving for x:

180 - 9x + 31 + 180 - 4x - 33 + 180 - 7x + 2 = 180

- 20 x + 540 = 180

- 20 x = 180 - 540 (Subtracting 540 to both sides)

- 20 x = - 360

x = 18 (Dividing by - 20)

Proving that x = 18 is correct

180 - 9x + 31 + 180 - 4x - 33 + 180 - 7x + 2 = 180

180 - 9 (18) + 31 + 180 - 4 (18) - 33 + 180 - 7 (18) + 2 = 180

180 - 162 + 31 + 180 - 72 - 33 + 180 - 126 + 2 = 180

573 - 393 = 180

180 = 180

We proved that x = 18 is correct

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