Let’s go through each pair of angles one by one and decide if they are
adjacent,
vertical, or
linear.
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Definitions (simple version):
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Adjacent angles: Two angles that share a common vertex and a common side, but do not overlap.
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Vertical angles: Angles opposite each other when two lines cross. They are always equal.
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Linear pair: Two adjacent angles that form a straight line — their non-common sides are opposite rays. Their measures add up to 180°.
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Now let’s analyze each:
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1) Angles *a* and *b*
→ They share a vertex and a side. They are next to each other.
→ Not vertical (not opposite).
→ Not linear (they don’t form a straight line together — there’s space between the outer rays).
✔ Adjacent
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2) Angles *1* and *2*
→ These are formed by two intersecting lines.
→ Angle 1 is opposite angle 2? Actually, looking closely: angle 1 and angle 2 are across from each other at the intersection.
→ Yes, they are vertical angles.
✔ Vertical
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3) Angles *1* and *2*
→ They share a vertex and a side.
→ They are next to each other, no overlap.
→ Do they form a straight line? No — the outer rays go in different directions.
✔ Adjacent
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4) Angles *P* and *Q*
→ They share a vertex and a side.
→ Together, they form a straight line (the horizontal line).
→ So they are both adjacent AND form a linear pair.
But the question asks to identify as “adjacent, vertical, or linear” — and since “linear” is more specific here (because they form a straight line), we choose
linear.
✔ Linear
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5) Angles *a* and *b*
→ Share a vertex and a side.
→ Next to each other.
→ Don’t form a straight line.
✔ Adjacent
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6) Angles *A* and *B*
→ Formed by two crossing lines.
→ Angle A is directly opposite angle B.
→ These are vertical angles.
✔ Vertical
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7) Angles *P* and *Q*
→ Share a vertex and a side.
→ Together, they make a straight line (horizontal line with ray going down).
→ So they form a linear pair.
✔ Linear
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8) Angles *a* and *b*
→ Share a vertex and a side.
→ They are next to each other.
→ Do they form a straight line? The outer rays are not opposite — they’re bent.
→ So not linear. Not vertical.
✔ Adjacent
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Final Answers:
1) Adjacent
2) Vertical
3) Adjacent
4) Linear
5) Adjacent
6) Vertical
7) Linear
8) Adjacent
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Final Answer:
1) Adjacent
2) Vertical
3) Adjacent
4) Linear
5) Adjacent
6) Vertical
7) Linear
8) Adjacent
Parent Tip: Review the logic above to help your child master the concept of angle pairs worksheet.
