To find the unknown angle when given one angle (like 106°), you will typically follow these general steps, depending on the type of geometric figure or relationship you are dealing with. Here are the steps for common scenarios:
Step 1: Identify the Type of Angle Relationship
Determine the relationship between the known angle and the unknown angle. Common relationships include:
- Complementary angles (sum to 90°)
- Supplementary angles (sum to 180°)
- Angles in a triangle (sum to 180°)
- Vertical angles (equal)
- Angles on a straight line (sum to 180°)
Step 2: Set Up the Equation
Depending on the relationship:
- For complementary: \( \text{Unknown angle} = 90° - 106° \)
- For supplementary: \( \text{Unknown angle} = 180° - 106° \)
- For angles in a triangle (if one angle is known and it's a triangle): \( \text{Unknown angle} = 180° - (106° + \text{other known angle}) \)
- For vertical angles: The unknown angle is simply \( 106° \).
- For angles on a straight line: Set up the equation to reflect the straight line configuration.
Step 3: Solve for the Unknown Angle
Carry out the arithmetic to solve for the unknown angle.
Example Solutions:
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If it's supplementary: \[ \text{Unknown Angle} = 180° - 106° = 74° \]
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If it's complementary: \[ \text{Unknown Angle} = 90° - 106° \] (This results in a negative number, meaning there is no complementary angle here.)
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In a triangle with another known angle (let's say it's 30°): \[ \text{Unknown Angle} = 180° - (106° + 30°) = 44° \]
Step 4: Double-check your work
Ensure that the angle calculated corresponds correctly with the relationships in the diagram.
If you provide specific details about the diagram or the context (like if it involves triangles, parallel lines, etc.), I can give more tailored guidance!