Answer-
The length of PR is 7 units.
Solution-
Given,
in the ΔDEF,
m∠D = 25°, m∠E = 114°, DF = 21, DE = 15
in the ΔPQR,
m∠P = 25°, m∠Q = 114°, PR = x, PQ = 5
So, ΔDEF ~ ΔPQR by AA (Angle-Angle) similarity, as
- m∠D = m∠P = 25°
- m∠E =m∠Q = 114°
So, according to similarity
\(\Rightarrow \dfrac{DF}{PR}=\dfrac{DE}{PQ}=\dfrac{EF}{QR}\)
Putting the values,
\(\Rightarrow \dfrac{21}{x}=\dfrac{15}{5}\)
\(\Rightarrow x=\dfrac{21\times 5}{15}\)
\(\Rightarrow x=7\)
