Question

Find the missing variable. asap please!! THANK YOU

Answer 1

Answer: $x=44, y=\dfrac{106}{3}$

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

$\Rightarrow\ 6y-21=4x+15 \ \ (i) \ and \ \ 130=3x-2 \ \ (ii)$

From (ii)

$3x=130+2\\\\\Rightarrow\ 3x=132\\\\\Rightarrow\ x= 44$

Put this in (i), we get

$6y-21=4(44)+15\\\\6y-21=176+15\\\\6y-21=191\\\\6y=191+21\\\\6y=212\\\\\Rightarrow\ y=\dfrac{212}{6}\\\\\Rightarrow\ y=\dfrac{106}{3}$

Hence, $x=44, y=\dfrac{106}{3}$