Which pairs of non-overlapping angles share a ray to make a right angle? Select all that apply.

Question

Angle EGF and angle FGH are right angles with common side FG. Ray GJ intersects angle FGH and ray GK intersects angle FGH.

(1 point)
Responses

∠EGK
and ∠FGK

∠ E G K and ∠ F G K

∠EGK
and ∠JGK

∠ E G K and ∠ J G K

∠FGK
and ∠FGH

∠ F G K and ∠ F G H

∠JGH
and ∠FGJ

∠ J G H and ∠ F G J

∠JGK
and ∠JGH

∠ J G K and ∠ J G H
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Answer 1

To determine which pairs of non-overlapping angles share a ray to create a right angle, we first need to understand the relationships between the angles involved.

Given:

• Angle EGF and angle FGH are right angles sharing ray FG.
• Ray GJ intersects angle FGH.
• Ray GK intersects angle FGH.

Now let's analyze the potential pairs:

1. ∠EGK and ∠FGK

   • These angles do not share a ray with respect to creating a right angle; both include ray GK with segments extending in different directions.

2. ∠EGK and ∠FGK

   • This is the same pair as option 1.

3. ∠EGK and ∠JGK

   • Angle EGK includes ray GK and is not related to JGK since they are not adjacent.

4. ∠EGK and ∠JGK

   • This is a repetition of option 3.

5. ∠FGK and ∠FGH

   • Both share ray FG as a common side, thus this is a valid combination, but these angles are actually overlapping.

6. ∠FGK and ∠FGH

   • This is a repetition of option 5.

7. ∠JGH and ∠FGJ

   • Angles JGH intersects with FGJ but does not create a right angle.

8. ∠JGH and ∠FGJ

   • This is a repetition of option 7.

9. ∠JGK and ∠JGH

   • ∠JGK and ∠JGH both share ray GJ as a common side and they are non-overlapping, making it a valid pair for creating a right angle.

10. ∠JGK and ∠JGH

    • This is a repetition of option 9.

Thus, the valid pairs of non-overlapping angles that share a ray to make a right angle would be:

• ∠JGK and ∠JGH.

Remember to check for correctness in how angles interact with rays for future scenarios.