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available: sep 18, 2025 12:00am until dec 18, 2025 11:59pm
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what is m∠lqk?
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Explanation:

Step1: Note angle - relationship

Since $\angle LQK$ and $\angle GQL$ are complementary (as $\angle GQH = 90^{\circ}$), and $\angle LQK=(4n - 15)^{\circ}$, $\angle GQL=(3n)^{\circ}$, we know that $\angle LQK+\angle GQL = 90^{\circ}$.

Step2: Set up equation

So, $(4n - 15)+3n=90$.
Combining like - terms, we get $4n+3n-15 = 90$, which simplifies to $7n-15 = 90$.
Adding 15 to both sides: $7n=90 + 15=105$.
Dividing both sides by 7: $n = 15$.

Step3: Find $\angle LQK$

Substitute $n = 15$ into the expression for $\angle LQK$.
$\angle LQK=(4n - 15)^{\circ}=(4\times15-15)^{\circ}=(60 - 15)^{\circ}=45^{\circ}$.

Answer:

$45$