Question

question 1 - 9
directions: select all correct answers
three lines intersect as shown. compare each angle to \\( \angle a g b \\).

Explanation:

Step1: Recall definitions

• Complementary angles: sum to \(90^{\circ}\).
• Supplementary angles: sum to \(180^{\circ}\).
• Vertical angles: opposite angles formed by two intersecting lines.

Step2: Analyze \(\angle BGD\)

• \(\angle AGB+\angle BGD = 90^{\circ}\) (from the right - angle at \(G\) formed by \(AG\) and \(EG\) with part of the angles). So \(\angle BGD\) is complementary to \(\angle AGB\).

Step3: Analyze \(\angle DGE\)

• \(\angle AGB+\angle DGE= 180^{\circ}\) (they form a linear pair). So \(\angle DGE\) is supplementary to \(\angle AGB\).

Step4: Analyze \(\angle FGA\)

• \(\angle AGB+\angle FGA = 90^{\circ}\) (from the right - angle at \(G\) formed by \(AG\) and \(EG\) with part of the angles). So \(\angle FGA\) is complementary to \(\angle AGB\).

Answer:

For \(\angle BGD\): Complementary
For \(\angle DGE\): Supplementary
For \(\angle FGA\): Complementary