Question

question 10 of 25 given the diagram below, hannah writes m∠1 + m∠4 = 180°, m∠2 + m∠5 = 180°, and m∠3 + m∠6 = 180°. which of the following reasons allows her to write these sums? a. addition property of equality b. definition of linear pair c. triangle sum theorem d. corresponding angles theorem

Explanation:

Step1: Identify angle - pair relationships

$\angle1$ and $\angle4$, $\angle2$ and $\angle5$, $\angle3$ and $\angle6$ are linear pairs.

Step2: Recall linear - pair property

A linear pair of angles is adjacent and supplementary (sum to 180°).

Step3: Match with options

The reason for $m\angle1 + m\angle4=180^{\circ}$, $m\angle2 + m\angle5 = 180^{\circ}$, and $m\angle3 + m\angle6=180^{\circ}$ is the definition of a linear pair.

Answer:

B. Definition of linear pair