x = 21
Solution:
In ΔABC,
BC = 96, AB = 63 and ∠ABC = 72°
In ΔDEF,
FE = 32, DE = x and ∠DEF = 72°
Given that ΔABC is similar to ΔDEF.
If two triangles are similar, then the corresponding sides are in proportion.
[tex]$\frac{AB}{EF} =\frac{AB}{DE}[/tex]
[tex]$\frac{96}{32} =\frac{63}{x}[/tex]
Do cross multiplication.
96x = 32 × 63
Divide by 96 on both sides.
x = 21
Hence the value of x is 21.
