Question

which is a true statement about the diagram? m∠5 + m∠6 = m∠1 m∠3 + m∠4 + m∠5 = 180° m∠1 + m∠2 = 180° m∠2 + m∠3 = m∠5

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 given triangle, $\angle5$ is an exterior angle and $\angle2$ and $\angle3$ are the non - adjacent interior angles.

Step2: Analyze each option

• Option 1: There is no such angle - sum relationship as $m\angle5 + m\angle6=m\angle1$.
• Option 2: $m\angle3 + m\angle4 + m\angle5

eq180^{\circ}$ since $\angle3,\angle4,\angle5$ do not form a straight - line or the interior angles of a triangle.

• Option 3: $m\angle1 + m\angle2

eq180^{\circ}$ as they are not supplementary angles in this context.

• Option 4: By the exterior - angle property of a triangle, $m\angle2 + m\angle3=m\angle5$.

Answer:

$m\angle2 + m\angle3=m\angle5$