Question

which statement regarding the diagram is true?
( m angle m k l + m angle m l k = m angle j k m )
( m angle k m l + m angle m l k = m angle j k m )
( m angle m k l + m angle m l k = 180 ^ { circ } )
( m angle j k m + m angle m l k = 180 ^ { circ } )

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.

Step2: Identify the exterior angle and 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 $\angle MLK$.
By the exterior angle theorem, $m\angle JKM=m\angle KML + m\angle MLK$.

For the other options:

• Option 1: $m\angle MKL + m\angle MLK=m\angle JKM$ is wrong because $\angle MKL$ is adjacent to $\angle JKM$.
• Option 3: $m\angle MKL + m\angle MLK = 180^{\circ}$ is wrong. In a triangle, the sum of all three interior angles is $180^{\circ}$, not just two angles.
• Option 4: $m\angle JKM + m\angle MLK=180^{\circ}$ has no geometric basis from the properties of triangle angles.

Answer:

$m\angle KML + m\angle MLK = m\angle JKM$