Answer:
m∠B = 83°
EF = 10
Step-by-step explanation:
Two triangles are similar if their corresponding angles are the same size.
Therefore if ΔABC ~ ΔDEF then:
- ∠A ≅ ∠D = 24°
- ∠B ≅ ∠E
- ∠C ≅ ∠F = 73°
Interior angles of a triangle sum to 180°:
⇒ m∠A + m∠B + m∠C = 180°
⇒ 24° + m∠B + 73° = 180°
⇒ m∠B + 97° = 180°
⇒ m∠B = 83°
In similar triangles, corresponding sides are always in the same ratio.
Therefore if ΔABC ~ ΔDEF then:
⇒ AB : DE = BC : EF = CA : FD
⇒ 12 : DE = 8 : EF = 16 : 20
Therefore, to find the length of EF:
[tex]\implies \sf 8 : EF = 16 : 20[/tex]
[tex]\implies \sf \dfrac{8}{EF} = \dfrac{16}{20}[/tex]
[tex]\implies \sf 8 \cdot 20= 16 \cdot EF[/tex]
[tex]\implies \sf160= 16 \cdot EF[/tex]
[tex]\implies \sf EF=\dfrac{160}{16}[/tex]
[tex]\implies \sf EF=10[/tex]
