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°

- 70

this is the answer for you hope it

(a) the volume of the cone is 20/3 in3

hence, option a is correct.