Question

given that m∠ljk = 40°, what is m∠jkl?

Explanation:

Step1: Recall circle - tangent property

Since $JL$ is tangent to the circle at $L$ and $KL$ is the radius, $\angle JLK = 90^{\circ}$.

Step2: Use angle - sum property of a triangle

In $\triangle JKL$, we know that the sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle LJK = 40^{\circ}$ and $m\angle JLK=90^{\circ}$. Using the formula $m\angle LJK + m\angle JKL+m\angle JLK = 180^{\circ}$, we can find $m\angle JKL$.
So, $m\angle JKL=180^{\circ}-m\angle LJK - m\angle JLK$.
Substitute the known values: $m\angle JKL = 180^{\circ}-40^{\circ}-90^{\circ}=50^{\circ}$.

Answer:

$50^{\circ}$