Question

which statement regarding the diagram is true?

m∠mkl + m∠mlk = m∠jkm

m∠kml + m∠mlk = m∠jkm

m∠mkl + m∠mlk = 180°

m∠jkm + m∠mlk = 180°

Explanation:

Step1: Recall the exterior - angle theorem

The exterior - angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
In \(\triangle MKL\), \(\angle JKM\) is an exterior angle. The two non - adjacent interior angles to \(\angle JKM\) are \(\angle KML\) and \(\angle MLK\).

Step2: Analyze each option

• For the option \(m\angle MKL + m\angle MLK=m\angle JKM\): \(\angle MKL\) is adjacent to \(\angle JKM\), so this does not follow the exterior - angle theorem.
• For the option \(m\angle KML + m\angle MLK=m\angle JKM\): By the exterior - angle theorem, since \(\angle JKM\) is an exterior angle of \(\triangle MKL\) and \(\angle KML\) and \(\angle MLK\) are the two non - adjacent interior angles, \(m\angle KML + m\angle MLK=m\angle JKM\).
• For the option \(m\angle MKL + m\angle MLK = 180^{\circ}\): \(\angle MKL\) and \(\angle MLK\) are two angles of \(\triangle MKL\), and \(m\angle MKL+m\angle MLK+m\angle KML=180^{\circ}\) (angle - sum property of a triangle), not \(m\angle MKL + m\angle MLK = 180^{\circ}\).
• For the option \(m\angle JKM + m\angle MLK=180^{\circ}\): There is no such relationship based on the properties of triangles (angle - sum property or exterior - angle theorem) for these two angles.

Answer:

\(m\angle KML + m\angle MLK=m\angle JKM\)