In triangle K M L, when considering the exterior angle \( \angle JKM \) formed by extending line \( LK \) through point \( J \), the following relationships hold true based on the properties of triangles and exterior angles.
The exterior angle theorem states that the measure of an exterior angle (in this case, \( \angle JKM \)) is equal to the sum of the measures of the two remote interior angles (the angles inside the triangle that are not adjacent to the exterior angle). In triangle K M L, the two remote interior angles are \( \angle MKL \) and \( \angle KML \).
Thus, we can say:
\[ m\angle JKM = m\angle MKL + m\angle KML \]
Now let's analyze the statements you provided:
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m∠MKL + m∠MLK = m∠JKM - This is incorrect because \( \angle MLK \) is not one of the two angles contributing to the exterior angle.
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m∠KML + m∠MLK = m∠JKM - This is also incorrect because \( \angle MLK \) is not one of the angles that adds to the exterior angle \( \angle JKM \).
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m∠MKL + m∠MLK = 180° - This is incorrect, as it is not necessarily true for the angles inside the triangle.
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m∠JKM + m∠MLK = 180° - This is correct because the exterior angle \( \angle JKM \) and the adjacent interior angle \( \angle MLK \) (being on the same line) will sum to \( 180° \).
Therefore, the correct statement is:
m∠JKM + m∠MLK = 180°.