Question

congruent triangles (topic 5)
△jkl and △lmn are shown.
what is the m∠kjl? (type only the number.)
m∠kjl =

Explanation:

Step1: Identify congruent parts

Since $\triangle{JKL}\cong\triangle{LMN}$ (by the markings of equal - sides), corresponding angles are equal.

Step2: Recall angle - sum property

In $\triangle{JKL}$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle{KJL}=\angle{MLN}=x$.
We know $\angle{JKL} = 72^{\circ}$, and assume the third - angle in $\triangle{JKL}$ is $\angle{KLJ}$.
Since the triangles are congruent, we can also use the fact that if we consider the angle - sum in $\triangle{JKL}$: $x + 72^{\circ}+\angle{KLJ}=180^{\circ}$.
Also, from the congruence of the triangles, we can note that the un - named angles are equal. In an isosceles - like situation (from the side - markings), we know that $\angle{KJL}=\angle{MLN}$.
Since the sum of angles in a triangle is $180^{\circ}$ and using the congruence of the triangles, we can find that $\angle{KJL}=(180 - 72)\div2$.

Step3: Calculate the angle

$x=\frac{180 - 72}{2}=\frac{108}{2}=54$.

Answer:

54