∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 . What is the value of x?

1 answer:

3 0

We know that ∠E = ∠F because of the vertical angle theorem.

Using substitution we get 8x + 8 = 2x + 38

Solve for x.

8x + 8 = 2x + 38
8x = 2x = 30 <-- Subtract 8 from each side
6x = 30 <-- Subtract 2x from each side
x = 5 <-- Divide both sides by 6

So, x is equal to 5.

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Given:

Given that the figure of similar triangles.

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The midpoint of AB is M(1, 3). If the coordinates of A are(4,1), what are the coordinates of B?

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Answer:

B(-2,5)

Step-by-step explanation:

$\frac{x + 4}{2} = 1 \\ 2 \times \frac{x + 4}{2} = 1 \times 2 \\ x + 4 = 2 \\ x = 2 - 4 \\ x = - 2 \\ \frac{y + 1}{2} = 3 \\ 2 \times \frac{y + 1}{2} = 3 \times 2 \\ y + 1 = 6 \\ y = 6 - 1 \\ y = 5$