Question

which statement regarding the diagram is true?
○ ( m angle mathrm{mkl}+m angle mathrm{mlk}=m angle mathrm{jkm} )
○ ( m angle mathrm{kml}+m angle mathrm{mlk}=m angle mathrm{jkm} )
○ ( m angle mathrm{mkl}+m angle mathrm{mlk}=180^{circ} )
○ ( m angle mathrm{jkm}+m angle mathrm{mlk}=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.

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

• Option 1: \(\angle MKL\) and \(\angle MLK\) are not the two non - adjacent interior angles to \(\angle JKM\). So, \(m\angle MKL + m\angle MLK

eq m\angle JKM\)

• Option 2: By the exterior - angle theorem, for \(\triangle MKL\) with exterior angle \(\angle JKM\), \(m\angle KML+m\angle MLK = m\angle JKM\)
• Option 3: \(\angle MKL+\angle MLK+\angle KML = 180^{\circ}\) (angle - sum property of a triangle). So, \(m\angle MKL + m\angle MLK

eq180^{\circ}\)

• Option 4: There is no such relationship \(m\angle JKM + m\angle MLK=180^{\circ}\) based on the properties of triangle angles

Answer:

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