Question

which statements are always true regarding the diagram? select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 = 180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Explanation:

Step1: Recall exterior - angle property

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. In the triangle with angles 2, 3, 5, angle 6 is an exterior angle. So, $m\angle2 + m\angle3=m\angle6$.

Step2: Recall linear - pair property

A linear pair of angles is supplementary. Angles 5 and 6 form a linear pair, so $m\angle5 + m\angle6 = 180^{\circ}$.

Step3: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. For the triangle with interior angles 2, 3, 5, $m\angle2 + m\angle3 + m\angle5=180^{\circ}$.

Answer:

$m\angle5 + m\angle6 = 180^{\circ}$, $m\angle2 + m\angle3=m\angle6$, $m\angle2 + m\angle3 + m\angle5 = 180^{\circ}$