Question

question
△zhs≅△kug. if m∠s = 148° and m∠h = 23°, find m∠k.
answer attempt 2 out of 5
m∠k can be determined. m∠k = □°.

Explanation:

Step1: Recall angle - congruence property

Since $\triangle ZHS\cong\triangle KUG$, corresponding angles are congruent. So $\angle H\cong\angle U$, $\angle S\cong\angle G$, and $\angle Z\cong\angle K$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. In $\triangle ZHS$, we know $m\angle S = 148^{\circ}$ and $m\angle H=23^{\circ}$. Let $m\angle Z = x$. Then $x + 148^{\circ}+23^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle Z$

$x=180^{\circ}-(148^{\circ} + 23^{\circ})=180^{\circ}-171^{\circ}=9^{\circ}$.

Step4: Find $m\angle K$

Since $\angle Z\cong\angle K$, $m\angle K=m\angle Z = 9^{\circ}$.

Answer:

$9$