Geometry

Question Analysis

This question involves the concepts of vertical angles, linear pairs, complementary angles, and obtuse angles.

Key Concept Explanation

Vertical Angles: Formed when two lines intersect, vertical angles are opposite each other and have equal measures.

Linear Pair: A pair of adjacent angles (sharing a common vertex and a common side) whose non - common sides form a straight line. The sum of angles in a linear pair is 180°.

Complementary Angles: Two angles whose sum is 90°.

Obtuse Angles: Angles with a measure greater than 90° and less than 180°.

Step - by - Step Solution

1. Analyze the position of ∠f and ∠g:

∠f and ∠g share a common vertex and a common side, so they are adjacent.

B.Their non - common sides form a straight line. By the definition of a linear pair, ∠f and ∠g are a linear pair.

A.They are not vertical angles as they are adjacent, not opposite each other.

C.There is no indication that their sum is 90°, so they are not complementary angles.

D.We cannot determine if they...