Question
Lines a and b are horizontal and parallel to each other. Line a contains points L and M and line b contains points O and N. Line c is diagonal and intersects line a at point X and line b and point Z. It also contains points H and G. Line d is diagonal and intersects line a at point X and line b at point Y. It also contains points J and K. Triangle X Y Z is created by the lines.
Which represents an exterior angle of triangle XYZ?
∠LXZ
∠JXM
∠JXZ
∠HXJ
Which represents an exterior angle of triangle XYZ?
∠LXZ
∠JXM
∠JXZ
∠HXJ
Answers
GPT-4o mini
To determine which angle represents an exterior angle of triangle XYZ, we need to understand the concept of exterior angles in relation to a triangle. An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side.
In triangle XYZ, the external angles can be defined as follows:
- **∠LXZ**: This angle is formed by line a and line c. It does not involve the extension of one of the sides of triangle XYZ, so it is not an exterior angle to the triangle.
- **∠JXM**: This angle is formed by line d (which intersects line a at point X) and the line extending from point J through X. This angle can also be considered as an exterior angle since it is formed outside of triangle XYZ.
- **∠JXZ**: This angle is inside triangle XYZ, as it is formed by sides XJ and XZ. Therefore, it is not an exterior angle.
- **∠HXJ**: This angle is also formed outside of triangle XYZ, but it involves point H, which does not play a role in the construction of triangle XYZ.
Given the definitions, **∠JXM** stands out as the angle that can be considered an exterior angle of triangle XYZ formed by the extension of side XJ outside the triangle.
Therefore, the answer is **∠JXM**.
In triangle XYZ, the external angles can be defined as follows:
- **∠LXZ**: This angle is formed by line a and line c. It does not involve the extension of one of the sides of triangle XYZ, so it is not an exterior angle to the triangle.
- **∠JXM**: This angle is formed by line d (which intersects line a at point X) and the line extending from point J through X. This angle can also be considered as an exterior angle since it is formed outside of triangle XYZ.
- **∠JXZ**: This angle is inside triangle XYZ, as it is formed by sides XJ and XZ. Therefore, it is not an exterior angle.
- **∠HXJ**: This angle is also formed outside of triangle XYZ, but it involves point H, which does not play a role in the construction of triangle XYZ.
Given the definitions, **∠JXM** stands out as the angle that can be considered an exterior angle of triangle XYZ formed by the extension of side XJ outside the triangle.
Therefore, the answer is **∠JXM**.