Exterior Angles of Polygons Score1/2 Penalty: mone Question Watch Video Show Eramples The exterior angle of a regular polygon measures $$ 40^{\circ} $$. How many sides does the polygon have? Zalyers Priyens Answer stempt lout of 2 Falygons (Level2) Submit tnower

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UpStudy AI · Accepted Answer

**Step 1:**  
The formula for the exterior angle $$ E $$ of a regular polygon with $$ n $$ sides is:  
$$
E = \frac{360^\circ}{n}
$$

**Step 2:**  
We are given $$ E = 40^\circ $$. Substitute this value into the formula to form the equation:  
$$
\frac{360^\circ}{n} = 40^\circ
$$

**Step 3:**  
Solve for $$ n $$ by multiplying both sides of the equation by $$ n $$:  
$$
360^\circ = 40^\circ \times n
$$

**Step 4:**  
Divide both sides by $$ 40^\circ $$ to isolate $$ n $$:  
$$
n = \frac{360^\circ}{40^\circ}
$$

**Step 5:**  
Compute the result:  
$$
n = 9
$$

The polygon has $$ 9 $$ sides.
The polygon has 9 sides.

Exterior Angles of Polygons Score1/2 Penalty: mone Question Watch Video Show Eramples The exterior angle of a regular polygon measures \( 40^{\circ} \). How many sides does the polygon have? Zalyers Priyens Answer stempt lout of 2 Falygons (Level2) Submit tnower

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