To determine the number of sides in a polygon given that the sum of its interior angles is 20 right angles, we can follow these steps: ### Step 1: Understand the Relationship Between Interior Angles and Sides The formula for the sum of the interior angles \( S \) of a polygon with \( n \) sides is given by: \[ S = (n - 2) \times 180^\circ \] This formula arises from the fact that a polygon can be divided into \( n - 2 \) triangles, and since each triangle has a sum of angles equal to \( 180^\circ \), we multiply the number of triangles by \( 180^\circ \). ### Step 2: Convert Right Angles to Degrees Since the problem states that the sum of the interior angles is 20 right angles, we need to convert this into degrees. A right angle is \( 90^\circ \), so: \[ 20 \text{ right angles} = 20 \times 90^\circ = 1800^\circ \] ### Step 3: Set Up the Equation Now we can set the sum of the interior angles equal to \( 1800^\circ \): \[ (n - 2) \times 180^\circ = 1800^\circ \] ### Step 4: Solve for \( n \) To find \( n \), we first divide both sides of the equation by \( 180^\circ \): \[ n - 2 = \frac{1800^\circ}{180^\circ} = 10 \] Next, we add 2 to both sides: \[ n = 10 + 2 = 12 \] ### Conclusion Thus, the polygon has **12 sides**. Therefore, the correct option is: **A. 12** ### Step 5: Analyze Other Options Now, let's examine the other options to understand why they are incorrect: - **B. 20**: If we assume the polygon has 20 sides, the sum of the interior angles would be: \[ (20 - 2) \times 180^\circ = 18 \times 180^\circ = 3240^\circ \] This is much greater than \( 1800^\circ \). - **C. 40**: For a polygon with 40 sides, the sum of the interior angles would be: \[ (40 - 2) \times 180^\circ = 38 \times 180^\circ = 6840^\circ \] Again, this is far greater than \( 1800^\circ \). - **D. 10**: If the polygon has 10 sides, the sum of the interior angles would be: \[ (10 - 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ \] This is still less than \( 1800^\circ \). ### Revision Summary - The sum of the interior angles of a polygon is calculated using the formula \( S = (n - 2) \times 180^\circ \). - 20 right angles convert to \( 1800^\circ \). - Solving the equation \( (n - 2) \times 180^\circ = 1800^\circ \) gives \( n = 12 \). - The correct answer is **A. 12**, while the other options do not satisfy the angle condition.