What is the sum of the interior angle measures of this polygon?
Understand the Problem
The question is asking for the sum of the interior angle measures of a convex polygon, which is represented in the diagram as a rhombus. To solve this, we will use the formula for the sum of the interior angles of a polygon, which is (n - 2) * 180°, where n is the number of sides.
Answer
The sum of the interior angle measures is $360°$.
Answer for screen readers
The sum of the interior angle measures of this polygon is $360°$.
Steps to Solve
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Identify the number of sides (n) In the diagram, the polygon shown is a rhombus, which has 4 sides. Therefore, $n = 4$.
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Apply the formula for the sum of interior angles The formula for the sum of the interior angles of a polygon is given by: $$ \text{Sum} = (n - 2) \times 180° $$ Substituting the value of $n$: $$ \text{Sum} = (4 - 2) \times 180° $$
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Calculate the sum Now, calculate the sum: $$ \text{Sum} = 2 \times 180° = 360° $$
The sum of the interior angle measures of this polygon is $360°$.
More Information
The sum of the interior angles formula can be applied to any polygon, not just a rhombus. For a polygon with any number of sides, this formula helps in determining the total interior angle measurement effectively.
Tips
- Miscounting sides: Ensure the number of sides is accurately counted; a rhombus has 4 sides, not 3 or 5.
- Incorrectly applying the formula: Remember to subtract 2 from the number of sides before multiplying by 180°.
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