Use the following diagram to answer questions

9514 1404 393

Step-by-step explanation:

17c. We cannot see the entire diagram, but based on what we can see, if we assume that segments FG and DH are parallel, then angles D and G correspond. The similarity statement is then ...

  ΔDEH ~ ΔGEF

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Corresponding angles are congruent, and are listed in the same order in the similarity statement. This means we have ...

  ∠D ≅ ∠G = 89° . . . . answer to 17b

  ∠E ≅ ∠E = 69°

  ∠H ≅ ∠F = 22° . . . . answer to 17a

Additional comment

The second choice listed for part 17c can be rejected simply on the basis that ΔEGH does not exist in the figure. Points G and H are not in the same triangle.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .