Which statements regarding the diagram are true? Check all that apply. XFG is an interior angle of AEFG. EFG is an interior angle of AEFG. FEZ is an exterior angle of AEFG. YGE is an exterior angle of AEFG. LEGF and angle FGY are supplementary angles. FEG and FGE are supplementary angles. Qua Chedl VWa Uununae E
The Correct Answer and Explanation is:
Based on the diagram, the true statements are:
- XFG is an interior angle of AEFG
- EFG is an interior angle of AEFG
- FEZ is an exterior angle of AEFG
- YGE is an exterior angle of AEFG
The false statements are:
- LEGF and angle FGY are supplementary angles
- FEG and FGE are supplementary angles
Explanation:
To determine which angles are interior, exterior, or supplementary, we must first understand the geometric relationships within quadrilateral AEFG.
An interior angle lies inside the polygon and is formed where two sides meet. In this case:
- ∠XFG lies inside the polygon at vertex F, between segments XF and FG. Since point X lies along AE, segment XF is part of AE, so ∠XFG is part of polygon AEFG.
- ∠EFG is located at vertex F as well, formed by segments EF and FG, both of which are sides of AEFG. So ∠EFG is also an interior angle.
An exterior angle is created when one side of a polygon is extended past a vertex, and the angle is formed between this extension and an adjacent side:
- ∠FEZ is an exterior angle because segment EZ extends side EF beyond point E and forms an angle with side FG.
- ∠YGE is another exterior angle since segment YG extends side FG beyond point G and meets segment GE.
Supplementary angles are two angles whose measures add up to 180 degrees. In this case:
- LEGF is not a clearly defined angle in the diagram. Even assuming it refers to a combination of angles around point G or F, there is no adequate justification to pair it with ∠FGY and say they sum to 180 degrees.
- FEG and FGE are adjacent angles within triangle FEG and together form the interior of the triangle, meaning their measures must sum to less than 180 degrees. Therefore, they are not supplementary.
