Question

$\overleftrightarrow{km}$ is tangent to $\odot j$. what is $m\angle m$?
$m\angle m = \square^\circ$

Explanation:

Step1: Use the property of tangent and radius

Since \( \overleftrightarrow{KM} \) is tangent to \( \odot J \) at \( K \), then \( JK\perp KM \), so \( \angle K = 90^{\circ} \).

Step2: Use the angle - sum property of a triangle

In \( \triangle JKM \), we know that the sum of the interior angles of a triangle is \( 180^{\circ} \). Given \( \angle JNK = 60^{\circ} \) and \( JK = JN \) (radii of the same circle), so \( \angle JKN=\angle JNK = 60^{\circ} \).
In \( \triangle KMN \), we use the formula \( \angle M=180^{\circ}-\angle K - \angle JNK\). Substitute \( \angle K = 90^{\circ} \) and \( \angle JNK = 60^{\circ} \) into the formula.

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Answer:

\(30\)