Answer:
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°
