Question

which is a true statement about the diagram?
( m angle 5 + m angle 6 = m angle 1 )
( m angle 3 + m angle 4 + m angle 5 = 180 ^ { circ } )
( m angle 1 + m angle 2 = 180 ^ { circ } )
( m angle 2 + m angle 3 = m angle 5 )

Explanation:

Step1: Analyze the first option

By the exterior - angle theorem, \(m\angle5 + m\angle6=m\angle4
eq m\angle1\) (since \(\angle1\) and \(\angle4\) are not related in this simple sum way from the diagram).

Step2: Analyze the second option

\(m\angle3 + m\angle4 + m\angle5
eq180^{\circ}\). Because \(\angle3\), \(\angle4\), and \(\angle5\) are not angles of a triangle. The sum of interior angles of a triangle is \(180^{\circ}\), but these angles do not form a triangle.

Step3: Analyze the third option

\(m\angle1 + m\angle2 = 180^{\circ}\) by the definition of a linear pair. A linear pair of angles is adjacent and supplementary (their sum is \(180^{\circ}\)).

Step4: Analyze the fourth option

By the exterior - angle theorem, \(m\angle2 + m\angle3=m\angle4
eq m\angle5\) (since \(\angle4\) and \(\angle5\) are not equal from the diagram).

Answer:

\(m\angle1 + m\angle2 = 180^{\circ}\)