Question

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

Explanation:

Step1: Identify tangent and radius

Line \( JL \) is tangent to the circle at \( L \), so \( KL \perp JL \) (radius is perpendicular to tangent at point of contact), meaning \( \angle KLJ = 90^\circ \).

Step2: Use triangle angle sum

In \( \triangle JKL \), we know \( \angle LJK = 40^\circ \) and \( \angle KLJ = 90^\circ \). The sum of angles in a triangle is \( 180^\circ \). Let \( \angle JKL = x \). Then:
\[
40^\circ + 90^\circ + x = 180^\circ
\]

Step3: Solve for \( x \)

Simplify the equation:
\[
130^\circ + x = 180^\circ
\]
Subtract \( 130^\circ \) from both sides:
\[
x = 180^\circ - 130^\circ = 50^\circ
\]

Answer:

\( 50^\circ \)