If a & b forms a pair of adjacent angles then which figures proves it .

Options

A.
B.
C.
D.

Answer

To determine which figures prove that angles A and B form a pair of adjacent angles, we need to follow a systematic approach. Here’s a step-by-step solution:

### Step 1: Understand the Definition of Adjacent Angles
Adjacent angles are two angles that have a common vertex and a common arm, but do not overlap.

**Hint:** Remember, adjacent angles share a side but do not share the space between them.

### Step 2: Analyze Each Figure
We will examine each figure (let's call them Figure A, Figure B, Figure C, and Figure D) to see if they meet the criteria for adjacent angles.

**Hint:** Look for a common vertex and a common arm in each figure.

### Step 3: Check Figure A
- In Figure A, check if angles A and B share a common vertex.
- Check if they have a common arm.
- If they do not share a common vertex or arm, they are not adjacent angles.

**Conclusion for Figure A:** Angles A and B do not form adjacent angles.

### Step 4: Check Figure B
- In Figure B, check if angles A and B share a common vertex.
- Check if they have a common arm.
- If they share both, then they are adjacent angles.

**Conclusion for Figure B:** Angles A and B form a pair of adjacent angles.

### Step 5: Check Figure C
- In Figure C, check if angles A and B share a common vertex.
- Check if they have different arms.
- If they have a common vertex and different arms, they are adjacent angles.

**Conclusion for Figure C:** Angles A and B form a pair of adjacent angles.

### Step 6: Check Figure D
- In Figure D, check if angles A and B share a common vertex.
- Check if they have a common arm.
- If they have both, they are adjacent angles.

**Conclusion for Figure D:** Angles A and B form a pair of adjacent angles.

### Final Answer
From the analysis, Figures B and C prove that angles A and B form a pair of adjacent angles.

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