Question

skillstream: special angle pairs formed by intersecting lines
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complementary

supplementary

vertical

adjacent

none

∠6 and ∠9 | □ | □ | □ | □ | ✔️
∠8 and ∠9 | □ | □ | □ | ✔️ | □
∠7 and ∠8 | □ | ✔️ | □ | ✔️ | □
∠6 and ∠8 | □ | □ | ✔️ | □ | □
∠9 and ∠10 | □ | □ | □ | □ | □

Explanation:

To solve this, we analyze each angle pair using definitions:

1. $\boldsymbol{\angle 6}$ and $\boldsymbol{\angle 9}$

• Complementary: Sum to $90^\circ$? No info.
• Supplementary: Sum to $180^\circ$? No.
• Vertical: Opposite angles? No.
• Adjacent: Share a side/vertex? No.
• Thus, None (already checked).

2. $\boldsymbol{\angle 8}$ and $\boldsymbol{\angle 9}$

• Adjacent: Share a common side and vertex (form a linear pair? Visually, they share a side/vertex). So Adjacent is correct (already checked).

3. $\boldsymbol{\angle 7}$ and $\boldsymbol{\angle 8}$

• Supplementary: Sum to $180^\circ$ (they form a linear pair, so supplementary).
• Adjacent: Share a side/vertex (yes, adjacent). Both checked, correct.

4. $\boldsymbol{\angle 6}$ and $\boldsymbol{\angle 8}$

• Vertical Angles: Opposite angles formed by intersecting lines. $\angle 6$ and $\angle 8$ are vertical (already checked, correct).

5. $\boldsymbol{\angle 9}$ and $\boldsymbol{\angle 10}$

• Need to check:
• Complementary: No.
• Supplementary: If they form a linear pair, sum to $180^\circ$? Visually, likely supplementary (and adjacent). But the boxes are empty, so we check:
• If they are a linear pair, Supplementary and Adjacent apply. But based on the diagram (assuming a straight line), $\angle 9$ and $\angle 10$:
• Supplementary: Sum to $180^\circ$ (linear pair).
• Adjacent: Share a side/vertex.

Final Checks (assuming the diagram has straight lines):

• $\angle 9$ and $\angle 10$: Mark Supplementary and Adjacent (if they form a linear pair).

But based on the given checks:

• $\angle 6$ & $\angle 9$: None (correct).
• $\angle 8$ & $\angle 9$: Adjacent (correct).
• $\angle 7$ & $\angle 8$: Supplementary + Adjacent (correct).
• $\angle 6$ & $\angle 8$: Vertical (correct).
• $\angle 9$ & $\angle 10$: If linear, mark Supplementary and Adjacent.

(If the task is to verify/check, the existing checks for $\boldsymbol{\angle 8 \& \angle 9}$, $\boldsymbol{\angle 7 \& \angle 8}$, $\boldsymbol{\angle 6 \& \angle 8}$ are correct. For $\boldsymbol{\angle 9 \& \angle 10}$, mark Supplementary and Adjacent if they are a linear pair.)

Answer:

To solve this, we analyze each angle pair using definitions:

1. $\boldsymbol{\angle 6}$ and $\boldsymbol{\angle 9}$

• Complementary: Sum to $90^\circ$? No info.
• Supplementary: Sum to $180^\circ$? No.
• Vertical: Opposite angles? No.
• Adjacent: Share a side/vertex? No.
• Thus, None (already checked).

2. $\boldsymbol{\angle 8}$ and $\boldsymbol{\angle 9}$

• Adjacent: Share a common side and vertex (form a linear pair? Visually, they share a side/vertex). So Adjacent is correct (already checked).

3. $\boldsymbol{\angle 7}$ and $\boldsymbol{\angle 8}$

• Supplementary: Sum to $180^\circ$ (they form a linear pair, so supplementary).
• Adjacent: Share a side/vertex (yes, adjacent). Both checked, correct.

4. $\boldsymbol{\angle 6}$ and $\boldsymbol{\angle 8}$

• Vertical Angles: Opposite angles formed by intersecting lines. $\angle 6$ and $\angle 8$ are vertical (already checked, correct).

5. $\boldsymbol{\angle 9}$ and $\boldsymbol{\angle 10}$

• Need to check:
• Complementary: No.
• Supplementary: If they form a linear pair, sum to $180^\circ$? Visually, likely supplementary (and adjacent). But the boxes are empty, so we check:
• If they are a linear pair, Supplementary and Adjacent apply. But based on the diagram (assuming a straight line), $\angle 9$ and $\angle 10$:
• Supplementary: Sum to $180^\circ$ (linear pair).
• Adjacent: Share a side/vertex.

Final Checks (assuming the diagram has straight lines):

• $\angle 9$ and $\angle 10$: Mark Supplementary and Adjacent (if they form a linear pair).

But based on the given checks:

• $\angle 6$ & $\angle 9$: None (correct).
• $\angle 8$ & $\angle 9$: Adjacent (correct).
• $\angle 7$ & $\angle 8$: Supplementary + Adjacent (correct).
• $\angle 6$ & $\angle 8$: Vertical (correct).
• $\angle 9$ & $\angle 10$: If linear, mark Supplementary and Adjacent.

(If the task is to verify/check, the existing checks for $\boldsymbol{\angle 8 \& \angle 9}$, $\boldsymbol{\angle 7 \& \angle 8}$, $\boldsymbol{\angle 6 \& \angle 8}$ are correct. For $\boldsymbol{\angle 9 \& \angle 10}$, mark Supplementary and Adjacent if they are a linear pair.)