Question

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

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 this case, \(\angle5\) is an exterior angle of the triangle, and \(\angle2\) and \(\angle3\) are the non - adjacent interior angles.

Step2: Analyze each option

• Option \(m\angle2 = m\angle3 = m\angle5\): This is incorrect. There is no reason to assume these angles are equal.
• Option \(m\angle3 + m\angle2=180^{\circ}\): This is incorrect. \(\angle3\) and \(\angle2\) are not supplementary in this context.
• Option \(m\angle3 + m\angle4 + m\angle5 = 180^{\circ}\): This is incorrect. \(\angle3\), \(\angle4\), and \(\angle5\) do not form a straight - line or a triangle interior angle sum in this way.
• Option \(m\angle5=m\angle3 + m\angle2\): This is correct as per the exterior angle theorem.

Answer:

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