Answer: [tex]x=44, y=\dfrac{106}{3}[/tex]
Step-by-step explanation:
GIven: Δ JKL ≅ Δ PQR, JK= 6y-21 , PQ = 4X+16, ∠L =(3x-2)
and ∠C = 130°.
Since corresponding parts of two congruent triangles are congruent.
So JK = PQ and ∠C = ∠L
[tex]\Rightarrow\ 6y-21=4x+15 \ \ (i) \ and \ \ 130=3x-2 \ \ (ii) \\\\\\[/tex]
From (ii)
[tex]3x=130+2\\\\\Rightarrow\ 3x=132\\\\\Rightarrow\ x= 44[/tex]
Put this in (i), we get
[tex]6y-21=4(44)+15\\\\6y-21=176+15\\\\6y-21=191\\\\6y=191+21\\\\6y=212\\\\\Rightarrow\ y=\dfrac{212}{6}\\\\\Rightarrow\ y=\dfrac{106}{3}[/tex]
Hence, [tex]x=44, y=\dfrac{106}{3}[/tex]
