If `angleABC+angleDEF=180^@`, name the pair of angles `angleABC` & `angleDEF`

Options

A. Adjacent Angles
B. Complementary Angles
C. Supplementary Angle
D. V.O.A

Answer

To solve the question, we need to identify the relationship between the two angles given that their sum is 180 degrees. Here's a step-by-step solution:

### Step 1: Understand the Given Information
We are given two angles, angle ABC and angle DEF, such that:
\[ \text{angle ABC} + \text{angle DEF} = 180^\circ \]

### Step 2: Identify the Types of Angle Relationships
We need to determine what type of angle pair angle ABC and angle DEF represent based on their sum.

### Step 3: Analyze the Options
1. **Adjacent Angles**: These are angles that share a common side and a common vertex. Since we do not have information that these angles are adjacent, we cannot classify them as adjacent angles.

2. **Complementary Angles**: These are angles whose sum is 90 degrees. Since the sum of angle ABC and angle DEF is 180 degrees, they cannot be complementary.

3. **Supplementary Angles**: These are angles whose sum is 180 degrees. Since the sum of angle ABC and angle DEF is exactly 180 degrees, they fit this definition.

4. **Vertically Opposite Angles**: These angles are formed when two lines intersect, creating pairs of opposite angles. We do not have enough information to conclude that angle ABC and angle DEF are vertically opposite angles.

### Step 4: Conclusion
Based on the analysis, since angle ABC and angle DEF add up to 180 degrees, we conclude that they are **supplementary angles**.

### Final Answer
The pair of angles angle ABC and angle DEF are **supplementary angles**.

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