Question

which is a true statement about the diagram?
$m\angle5 + m\angle6 = m\angle1$
$m\angle3 + m\angle4 + m\angle5 = 180^{circ}$
$m\angle1 + m\angle2 = 180^{circ}$
$m\angle2 + m\angle3 = m\angle5$

Explanation:

Step1: Use 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 the given diagram, \(\angle5\) is an exterior angle of the triangle with interior angles \(\angle2\) and \(\angle3\).
So, by the exterior angle theorem, \(m\angle2 + m\angle3 = m\angle5\).

Step2: Analyze other options

• For \(m\angle5 + m\angle6=m\angle1\): There is no geometric relationship (such as angle - addition or theorem) to support this. \(\angle1\), \(\angle5\) and \(\angle6\) are not related in this additive way.
• For \(m\angle3 + m\angle4 + m\angle5 = 180^{\circ}\): \(\angle3\), \(\angle4\) and \(\angle5\) do not form a triangle or a linear pair that would sum to \(180^{\circ}\).
• For \(m\angle1 + m\angle2 = 180^{\circ}\): \(\angle1\) and \(\angle2\) are not supplementary (they are not a linear pair).

Answer:

\(m\angle2 + m\angle3 = m\angle5\)