To prove that the triangles are similar by the sas similarity theorem, it needs to be proven that
j measures 60°.
j measures 30°.
i measures 60°.
i measures 30°.

I measures 60° ⇒ 3rd answer

Step-by-step explanation:

* Look to the attached figure

- To prove that the two triangles are similar by SAS we must to

  find two proportional pairs of corresponding side and the measure

  of the including angles between them are equal

- The given is:

  m∠ F = 60°

  EF = 40 , FG = 20

  HI = 20 , IJ = 10

- To prove that the Δ EFG is similar to Δ HIJ we must to prove

# EF/ HI = FG/IJ ⇒ two pairs of sides proportion

# m∠ F = m∠ I ⇒ including angles equal

∵ EF = 40 and HI = 20

∴ EF/HI = 40/20 = 2

∵ FG = 20 and IJ = 10

∴ FG/IJ = 20/10 = 2

∵ EF/HI = FG/IJ = 2

∴ The two pairs of sides are proportion

∵ ∠ F is the including angle between EF and FG

∵ ∠ I is the including angle between HI and IJ

∴ m∠ F must equal m∠ I

∵ m∠ F = 60° ⇒ given

∴ m∠ I = 60°

* I measures 60°

3201

step-by-step explanation:

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 .