Question

two opposite angles formed by intersecting lines are: mark only one oval. adjacent vertical linear pair supplementary 17. if two angles form a linear pair and one measures 75°, the other measures: mark only one oval. 15° 90° 105° 120° 18. which is an example of inductive reasoning? * mark only one oval. using definitions to prove a fact observing a pattern and making a conjecture using postulates to explain a theorem following logical steps to reach a conclusion

Explanation:

Step1: Recall angle - pair definitions

Two opposite angles formed by intersecting lines are vertical angles. Adjacent angles share a side and a vertex. A linear - pair of angles are adjacent and supplementary. Supplementary angles add up to 180°.

Step2: Solve for the second angle in a linear - pair

Let the two angles in the linear pair be \(x\) and \(y\). We know that \(x + y=180^{\circ}\). Given \(x = 75^{\circ}\), then \(y=180^{\circ}-75^{\circ}=105^{\circ}\).

Step3: Recall the definition of inductive reasoning

Inductive reasoning involves observing patterns and making general conjectures. Deductive reasoning uses definitions, postulates, and logical steps to prove facts or reach conclusions.

Answer:

1. B. Vertical
2. C. 105°
3. B. Observing a pattern and making a conjecture