Question

directions: select all correct answers
three lines intersect as shown. compare each angle to ∠agb
∠bgd
∠dge
∠fga
complementary
supplementary
vertical

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

eq90^{\circ}\), \(\angle AGB + \angle BGD
eq180^{\circ}\), \(\angle AGB\) and \(\angle BGD\) are not vertical angles.

Step3: Analyze \(\angle DGE\)

• \(\angle AGB+\angle DGE = 180^{\circ}\) (linear - pair), so \(\angle DGE\) is supplementary to \(\angle AGB\).

Step4: Analyze \(\angle FGA\)

• \(\angle AGB+\angle FGA=90^{\circ}\) (given right - angle at \(G\) where \(\angle FGE = 90^{\circ}\) and using angle - addition), so \(\angle FGA\) is complementary to \(\angle AGB\).

Answer:

	Complementary	Supplementary	Vertical
\(\angle DGE\)		\(\square\)
\(\angle FGA\)	\(\square\)