Question

what is m∠kjl? for items 3 - 4, use △jkl and △lmn shown.

Explanation:

Step1: Identify isosceles triangle

In $\triangle{JKL}$, since two - sides are congruent (marked with double - hash marks), $\triangle{JKL}$ is isosceles. Let the base - angles be $\angle{J}$ and $\angle{L}$, and the vertex - angle be $\angle{K}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. We know that $\angle{K}=72^{\circ}$. Let $\angle{J}=\angle{L}=x$. Then, by the angle - sum property of a triangle, $x + x+72^{\circ}=180^{\circ}$.

Step3: Solve the equation for $x$

Combining like terms, we get $2x=180^{\circ}-72^{\circ}=108^{\circ}$. Dividing both sides by 2, $x = 54^{\circ}$.

Answer:

$54^{\circ}$