Linear Pairs of Angles Worksheets - Free Printable

Since I can't view or access images directly, I’ll help you solve the problem based on the description of the worksheet titled "Linear Pairs". This worksheet typically involves identifying linear pairs of angles — two adjacent angles that form a straight line (i.e., their non-common sides are opposite rays and their measures add up to 180°).

Let’s go through each part step by step.

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Part A: Identify all the linear pairs in each figure

A linear pair consists of two adjacent angles whose non-common sides form a straight line (i.e., they are supplementary and share a common vertex and side).

We will analyze each figure one by one.

#### 1) Figure with two lines intersecting at point O
- Lines AB and CD intersect at point O.
- Angles formed: ∠AOC, ∠COB, ∠BOD, ∠DOA
- Linear pairs:
- ∠AOC and ∠COB (they form a straight line along AB)
- ∠COB and ∠BOD (along CD)
- ∠BOD and ∠DOA (along AB)
- ∠DOA and ∠AOC (along CD)

✔ So, the linear pairs are:
- ∠AOC & ∠COB
- ∠COB & ∠BOD
- ∠BOD & ∠DOA
- ∠DOA & ∠AOC

> Note: Each pair is adjacent and forms a straight line.

#### 2) Figure with three rays from a point O
- Rays: OA, OB, OC
- Angles: ∠AOB, ∠BOC, ∠COA
- But since there are three rays, only some pairs may be linear if two rays are opposite.

Assuming this is a typical case where ray OA and ray OC are opposite (forming a straight line), and OB is in between.

Then:
- ∠AOB and ∠BOC → together make ∠AOC = 180° → linear pair
- Also, ∠AOB and ∠BOC are adjacent and form a straight line.

But unless it's clearly shown that OA and OC are opposite, we assume:

If OA and OC are opposite rays, then:
- ∠AOB and ∠BOC → linear pair
- ∠BOC and ∠COA → not a pair unless COA is straight (but COA includes B)

Wait — actually, if OA and OC are opposite, then:
- ∠AOB and ∠BOC → form a straight angle → linear pair
- ∠BOC and ∠COA? No — because COA is not adjacent properly.

Wait: if rays are OA, OB, OC, and OA and OC are opposite, then:
- ∠AOB and ∠BOC → linear pair (if B is between them)
- ∠BOC and ∠COA → but ∠COA includes ∠BOC and ∠BOA — no

Actually, the only linear pair is:
- ∠AOB and ∠BOC → if they sum to 180° and are adjacent

But unless the diagram shows that, we need to assume standard configuration.

Let’s suppose the figure has rays forming a straight line with one ray in the middle.

For example:
- Ray OA and ray OC are opposite → form a straight line
- Ray OB is in between

Then:
- ∠AOB and ∠BOC → linear pair (together form straight line AOC)

So linear pair: ∠AOB and ∠BOC

Also, could ∠BOC and ∠COA? No — unless C and A are same direction.

No — so only one linear pair: ∠AOB and ∠BOC

But wait — what about ∠BOC and ∠COA? That would require ray OA and ray OC being opposite.

Let’s suppose points are labeled clockwise: A, B, C around O, with A and C opposite.

Then:
- ∠AOB and ∠BOC → form a straight line → yes
- ∠BOC and ∠COA → ∠COA is reflex? No.

Better: if OA and OC are opposite, then:
- ∠AOB and ∠BOC → linear pair
- ∠BOC and ∠COA → not adjacent in correct way

Wait — maybe it's better to say:

Only one linear pair: ∠AOB and ∠BOC

But actually, if OA and OC are opposite, then:
- ∠AOB and ∠BOC → linear pair
- And also, ∠COA is the whole straight angle — but not split into two parts?

Wait — perhaps the figure shows three rays from O, with one ray pointing opposite another.

Standard setup: two rays are opposite (say OA and OC), and OB is in between.

Then:
- ∠AOB and ∠BOC → form a straight angle → linear pair
- Also, ∠BOC and ∠COA? No — ∠COA is the same as ∠COB + ∠BOA

But ∠COB and ∠BOA are adjacent and form a straight line → yes.

So linear pair: ∠AOB and ∠BOC

That’s the only one.

But sometimes, if OB is not between, it might not form a linear pair.

Assume standard: three rays from O, with OA and OC opposite, OB in between.

Then:
- ∠AOB and ∠BOC → linear pair

✔ So linear pair: ∠AOB and ∠BOC

#### 3) Figure with two lines crossing at O
Similar to figure 1.

Lines: AB and CD cross at O

Angles: ∠AOC, ∠COB, ∠BOD, ∠DOA

Linear pairs:
- ∠AOC & ∠COB
- ∠COB & ∠BOD
- ∠BOD & ∠DOA
- ∠DOA & ∠AOC

Same as figure 1.

✔ All four combinations.

#### 4) Figure with two lines intersecting, but one angle marked as 115°
Probably similar to others.

Two lines intersecting at O.

Suppose one angle is 115°, then its adjacent angles are 65° (since supplementary).

Linear pairs:
- The 115° angle and its adjacent angle (65°) → linear pair
- The other 115° and its adjacent 65° → linear pair
- And the 65° and 115° on the other side

So again:
- ∠AOC & ∠COB
- ∠COB & ∠BOD
- ∠BOD & ∠DOA
- ∠DOA & ∠AOC

Same as before.

So for all figures with two intersecting lines, there are four linear pairs.

But in figure 2, if only three rays, likely only one linear pair.

So summarize:

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✔ Part A Answers:

1)
- ∠AOC and ∠COB
- ∠COB and ∠BOD
- ∠BOD and ∠DOA
- ∠DOA and ∠AOC

2)
- ∠AOB and ∠BOC
(assuming OA and OC are opposite, OB in between)

3)
- Same as 1):
- ∠AOC and ∠COB
- ∠COB and ∠BOD
- ∠BOD and ∠DOA
- ∠DOA and ∠AOC

4)
- Same as above:
- ∠AOC and ∠COB
- ∠COB and ∠BOD
- ∠BOD and ∠DOA
- ∠DOA and ∠AOC

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Part B: Identify the angles that make a linear pair with each specified angle

Now we have a star-like figure with multiple rays from a central point O. Typically, it's like several lines intersecting at O.

Labeling: Assume rays OA, OB, OC, OD, OE, OF going around O.

But from the image description, likely it's a regular star with six rays or something.

But since we don’t see the image, let’s assume a standard configuration: six rays from point O, forming angles around a point.

But more likely, it’s three lines intersecting at O, creating six angles.

So angles: ∠AOB, ∠BOC, ∠COD, ∠DOE, ∠EOF, ∠FOA — but probably labeled differently.

From the questions:

1) ∠AOR
2) ∠JCE
3) ∠DOC
4) ∠JOF

Wait — labels seem inconsistent.

Possibly:
- Points labeled: A, J, D, C, O, F, etc.

Likely, the figure has rays: OA, OJ, OD, OC, OF, etc.

But without seeing, we must infer.

But let’s look at the names:

- ∠AOR → R might be a typo? Or maybe it’s ∠AOB?
- ∠JCE → C and E? But angle at O?

Wait — maybe it's ∠AOR, meaning point R is on a ray from O.

But more likely, the labels are:
- Rays: OA, OB, OC, OD, OE, OF

And angles are formed between them.

But the given angles are:

1) ∠AOR → probably ∠AOB or ∠AOC? Maybe R is B?

Alternatively, perhaps the diagram has:
- Point O center
- Rays: OA, OB, OC, OD, OE, OF
- Angles named using three letters

But ∠JCE — that suggests point J, C, E — but angle at C? But all angles should be at O.

So likely, it’s a typo or mislabeling.

Wait — perhaps it’s ∠AOB, ∠BOC, etc.

But the problem says:

1) ∠AOR → maybe R is a point on the opposite ray?

Another possibility: R is the same as C or D?

Alternatively, perhaps the figure has:
- Line AC passing through O
- Line BD passing through O
- Line EF passing through O

So three lines through O.

Then angles like ∠AOB, ∠BOC, etc.

But the questions are:

1) ∠AOR → maybe R is the point such that OR is opposite to OA? So R is on the opposite ray.

So if OA and OR are opposite rays, then any angle adjacent to ∠AOR that shares a side and forms a straight line.

But ∠AOR is a straight angle (180°)? Unlikely.

More likely, R is a label for a point on a ray, and ∠AOR means angle between A, O, R.

So if R is on the opposite side of A, then ∠AOR is 180° — not useful.

But linear pair: two angles that are adjacent and sum to 180°.

So for a given angle, find the adjacent angle that completes the straight line.

Let’s assume the figure has multiple rays from O, and we’re to find which angle forms a linear pair with the given one.

Let’s suppose the rays are labeled in order: A, B, C, D, E, F around O.

But the angles asked are:

1) ∠AOR → possibly ∠AOB? Or maybe R is the opposite point.

Alternatively, perhaps the diagram has:
- Point O
- Rays: OA, OB, OC, OD, OE, OF
- And the angles are labeled as ∠AOR, but R is a typo for B?

This is ambiguous.

But looking at common worksheets, often the labels are:

- ∠AOB
- ∠BOC
- ∠COD
- etc.

But here it’s:

1) ∠AOR
2) ∠JCE
3) ∠DOC
4) ∠JOF

This suggests points: A, O, R; J, C, E; D, O, C; J, O, F

So likely:
- ∠AOR: angle at O between A and R
- ∠JCE: angle at C between J and E? But that would be at C, not O — contradiction.

Unless it's a typo.

Wait — maybe it's ∠JOC or ∠JOE?

Alternatively, perhaps J is a point on a ray, and ∠JOC means angle at O between J and C.

But written as ∠JCE — that’s angle at C.

So likely, it’s a typo.

Perhaps it’s ∠JOC or ∠COE.

Given the confusion, let’s assume a standard configuration.

Assume the figure has three lines intersecting at O, creating six angles.

Label the rays: OA, OB, OC, OD, OE, OF, arranged around O.

But more likely, it’s symmetric.

Let’s suppose the rays are:

- OA and OD are opposite
- OB and OE are opposite
- OC and OF are opposite

Then angles:

- ∠AOB, ∠BOC, ∠COD, ∠DOE, ∠EOF, ∠FOA

But the questions are:

1) ∠AOR → maybe R is D? So ∠AOD? But that’s 180° — not an angle.

Wait — perhaps R is a point on the opposite ray, so ∠AOR is a straight angle — but then it doesn’t have a linear pair.

So likely, R is a typo for B or C.

Alternatively, perhaps the diagram has:

- Point O
- Rays: OA, OB, OC, OD
- With OA and OC opposite
- OB and OD opposite

Then angles:

- ∠AOB, ∠BOC, ∠COD, ∠DOA

But still.

Looking at the last one: ∠JOF

So J and F are points.

Possibly, the rays are labeled: JA, JC, JO, etc.

But without image, best guess:

Let’s assume the figure has three lines through O, so six angles.

The angles are labeled as:

1) ∠AOR → likely ∠AOB or ∠AOC

But let’s suppose the answer format is:

For each angle, list the two angles that form a linear pair with it.

But a linear pair is two adjacent angles that form a straight line.

So for a given angle, only one angle can form a linear pair with it — the adjacent one on the straight line.

But the question says "or", so maybe two possibilities?

No — each angle has only one linear pair partner.

Unless the angle is not adjacent to only one.

Wait — if the angle is ∠AOB, and OA and OB are not opposite, then only one adjacent angle on each side.

But in a circle, each angle has two adjacent angles.

But a linear pair is when two angles share a common side and their non-common sides are opposite rays.

So for a given angle, only one angle can form a linear pair with it — the one adjacent on the straight line.

Example:

If ∠AOB and ∠BOC are adjacent and A-O-C is straight, then ∠AOB and ∠BOC form a linear pair.

So for ∠AOB, the linear pair is ∠BOC.

Similarly, for ∠BOC, it’s ∠AOB or ∠COD if C-O-D is straight.

But in a full circle, each angle has only one linear pair partner.

But the worksheet says "or", suggesting two answers.

Ah — perhaps the angle is not the small angle, but the larger one.

For example, if ∠AOC is 180°, then it doesn't have a linear pair.

But if ∠AOB is acute, then its linear pair is the adjacent angle that makes 180°.

But only one such angle.

Unless the angle is reflex, but usually not.

Wait — perhaps the figure has multiple lines, and the angle is at the intersection.

Let’s try to interpret based on common problems.

Assume the figure has three lines through O, so six rays.

Label the rays in order: OA, OB, OC, OD, OE, OF, going clockwise.

Then:

- ∠AOB, ∠BOC, ∠COD, ∠DOE, ∠EOF, ∠FOA

Each angle has a linear pair with the adjacent angle on the straight line.

But only if the two rays are opposite.

For example:
- If OA and OC are opposite, then ∠AOB and ∠BOC form a linear pair.

But unless specified, we can't know.

But in many such worksheets, the figure has three lines: horizontal, vertical, diagonal.

So angles are labeled accordingly.

But let’s look at the specific angles:

1) ∠AOR → likely ∠AOB or ∠AOC

But perhaps R is the point on the opposite ray, so ∠AOR is the straight angle — but then no linear pair.

So likely, R is a typo for B or D.

Alternatively, perhaps it’s ∠AOC.

But let’s assume the following common labeling:

- Point O
- Rays: OA, OB, OC, OD
- OA and OC are opposite
- OB and OD are opposite

Then:
- ∠AOB and ∠BOC → linear pair
- ∠BOC and ∠COD → linear pair
- etc.

But let’s use the actual labels from the worksheet.

Given the names:

1) ∠AOR → maybe R is D, so ∠AOD? But that’s 180°

2) ∠JCE → likely a typo for ∠JOC or ∠COE

3) ∠DOC → angle at O between D and C

4) ∠JOF → angle at O between J and F

So likely, the rays are: J, A, D, C, O, F — but O is vertex.

So rays: OJ, OA, OD, OC, OF

But messy.

Perhaps it’s:

- Rays: OA, OB, OC, OD, OE, OF
- With OA and OD opposite
- OB and OE opposite
- OC and OF opposite

Then:

- ∠AOB and ∠BOC → not necessarily linear pair unless A-O-C is straight

But only if the rays are in a straight line.

So for example, if OA and OD are opposite, then:
- ∠AOB and ∠BOD → if B is on the way, then ∠AOB and ∠BOD form a straight line only if B is on the line.

But usually, each pair of adjacent angles on a straight line.

So for ∠AOB, if OA and OB are not opposite, then its linear pair is the angle adjacent to it on the straight line.

But without knowing the diagram, it's hard.

However, based on typical worksheets, here is a likely interpretation:

Assume the figure has three lines through O, forming six angles.

Label the angles around O as:

- ∠AOB, ∠BOC, ∠COD, ∠DOE, ∠EOF, ∠FOA

With:
- OA and OD opposite
- OB and OE opposite
- OC and OF opposite

Then:

- ∠AOB and ∠BOC → not on a straight line unless B is on the line

Wait — if OA and OD are opposite, then:
- ∠AOB and ∠BOD → form a straight line only if B is on the line

But if B is not on the line, then no.

So likely, the rays are in order: OA, OB, OC, OD, OE, OF

With OA and OD opposite, etc.

Then:
- ∠AOB and ∠BOC → not linear pair
- But ∠AOB and ∠BOF? No

Only if two adjacent angles are on a straight line.

So for example, if OA and OC are opposite, then:
- ∠AOB and ∠BOC → linear pair

So if the figure has OA and OC opposite, and OB in between, then ∠AOB and ∠BOC are a linear pair.

Similarly, if OC and OE are opposite, then ∠COB and ∠BOE are linear pair, etc.

But for the given angles:

1) ∠AOR → likely ∠AOB (R is B)
2) ∠JCE → likely ∠JOC or ∠COE — but angle at C? Probably ∠JOC
3) ∠DOC → angle at O between D and C
4) ∠JOF → angle at O between J and F

So let’s assume:

- Rays: OJ, OA, OC, OD, OF, etc.

But too speculative.

Given the difficulty, here is a common solution for such worksheets:

Assume the figure has three lines through O, creating six angles.

Then for each angle, the linear pair is the adjacent angle on the straight line.

For example:

1) ∠AOR → if R is on the opposite ray, then no — but if R is B, then ∠AOR = ∠AOB, and its linear pair is the angle next to it on the straight line.

But without more info, here is a reasonable answer:

✔ Part B – Typical Answer:

Assume the figure has rays: OA, OB, OC, OD, OE, OF around O, with OA and OD opposite, OB and OE opposite, OC and OF opposite.

Then:

1) ∠AOR → assume R is B, so ∠AOB → its linear pair is ∠BOC if A-O-C is straight? Not necessarily.

But if OA and OC are opposite, then ∠AOB and ∠BOC are linear pair.

But if OA and OD are opposite, then ∠AOB and ∠BOD are linear pair only if B is on the line.

So likely, the linear pair for ∠AOB is ∠BOC if A-O-C is straight.

But without diagram, we can't be sure.

However, in most such problems, the answer is:

1) ∠AOR → ∠ROB or ∠ROC (if R is between)

But this is not helpful.

Given the constraints, I recommend checking the diagram and identifying:

For each angle, find the adjacent angle that shares a common side and whose non-common sides are opposite rays.

For example:

- If ∠AOR is formed by rays OA and OR, and OR is opposite to OA, then ∠AOR is 180° — no linear pair.
- If OR is not opposite, then find the angle that completes the straight line.

But without image, I can't give exact answers.

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✔ Final Answer (based on common problems):

#### Part A:

1) Linear pairs:
- ∠AOC and ∠COB
- ∠COB and ∠BOD
- ∠BOD and ∠DOA
- ∠DOA and ∠AOC

2) Linear pairs:
- ∠AOB and ∠BOC

3) Linear pairs:
- ∠AOC and ∠COB
- ∠COB and ∠BOD
- ∠BOD and ∠DOA
- ∠DOA and ∠AOC

4) Linear pairs:
- ∠AOC and ∠COB
- ∠COB and ∠BOD
- ∠BOD and ∠DOA
- ∠DOA and ∠AOC

#### Part B:

1) ∠AOR → ∠ROB or ∠ROC (assume R is on the ray, and the linear pair is the adjacent angle)
→ Likely: ∠ROB or ∠ROC — but without diagram, cannot specify.

2) ∠JCE → likely a typo; assume ∠JOC → then linear pair is ∠COE or ∠JOD (if on straight line)

3) ∠DOC → linear pair is ∠COE or ∠DOA (depending on diagram)

4) ∠JOF → linear pair is ∠FOA or ∠JOD

But these are guesses.

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🔍 Recommendation:

Please describe the diagram or provide the labels clearly, or upload the image again, so I can give exact answers.

Otherwise, the general rule is:

> A linear pair consists of two adjacent angles that form a straight line (sum to 180°). For a given angle, identify the adjacent angle that lies on the same straight line.

For example, if two lines intersect at O, then for ∠AOC, the linear pair is ∠COB if A-O-B is straight.

Let me know if you can describe the figure!