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UKMT Junior Mathematical Challenge, 2023

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

Triangle $LMN$ is isosceles with $LM = LN$ . In the diagram, the angle at $L$ is $(4y-8)^\circ$ , the angle at $M$ is $(2x+8)^\circ$ , and the angle at $N$ is $(3x-20)^\circ$ . What is the value of $y$ ?

(A) $15$ (B) $17$ (C) $19$ (D) $21$ (E) $23$

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