Question

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

Explanation:

Step1: Recognize isosceles triangle

In $\triangle{JKL}$, since $JK = KL$, $\triangle{JKL}$ is isosceles. So $\angle{KJL}=\angle{KLJ}$.

Step2: Use angle - sum property of a triangle

Let $\angle{KJL}=\angle{KLJ}=x$. In $\triangle{JKL}$, we know that $\angle{JKL} = 72^{\circ}$, and by the angle - sum property of a triangle ($\angle{JKL}+\angle{KJL}+\angle{KLJ}=180^{\circ}$), we have $72^{\circ}+x + x=180^{\circ}$.

Step3: Solve the equation

Combining like terms gives $72^{\circ}+2x = 180^{\circ}$. Subtract $72^{\circ}$ from both sides: $2x=180^{\circ}- 72^{\circ}=108^{\circ}$. Then divide both sides by 2: $x=\frac{108^{\circ}}{2}=54^{\circ}$.

Answer:

$54$