△ijk ≅ △wxy. what is m∠k?

Question

Accepted Answer

# Explanation:
## Step1: Use the property of congruent triangles
Since $\triangle IJK\cong\triangle WXY$, their corresponding angles are equal.
## Step2: Find the measure of $\angle K$
In $\triangle WXY$, using the angle - sum property of a triangle ($\angle Y+\angle W+\angle X = 180^{\circ}$), but we can also use the correspondence. $\angle K$ corresponds to $\angle X$.
In $\triangle WXY$, $\angle X=180^{\circ}-(78^{\circ} + 61^{\circ})$
$$
\begin{align*}
\angle X&=180^{\circ}-139^{\circ}\
&=41^{\circ}
\end{align*}
$$
Another way: Since $\triangle IJK\cong\triangle WXY$, $\angle I$ corresponds to $\angle W = 61^{\circ}$, $\angle J$ corresponds to $\angle Y=78^{\circ}$, and $\angle K$ corresponds to $\angle X$.
Using the angle - sum property of a triangle in $\triangle IJK$ ($\angle I+\angle J+\angle K=180^{\circ}$), $\angle K = 180^{\circ}-(61^{\circ}+78^{\circ})$
$$
\begin{align*}
\angle K&=180^{\circ}-139^{\circ}\
&=41^{\circ}
\end{align*}
$$

# Answer:
$41$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of congruent triangles

Step2: Find the measure of \(\angle K\)

Answer: