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Find the number of sides in a regular polygon if each of its interior angles is 144 degrees.
8
10
12
9
10
Given: Interior angle = 144° for a regular polygon
Interior angle = 144° for a regular polygon
\text{Interior angle}=\frac{(n-2)\times180°{n}
Exterior angle = 180°-144° = 36°, so n = 360°/36° = 10
Forgetting to divide the sum of interior angles by n when using the interior‑angle formula
Identify the given interior angle
The problem states that each interior angle of the regular polygon is 144°.
Given interior angle=144°
Apply the interior‑angle formula
For a regular polygon with n sides, interior angle I = \frac{(n-2)\times180°{n}. Set I=144° and solve for n.
\frac{(n-2)\times180°{n}=144°
Solve for n
Multiply both sides by n: (n−2)×180=144n. Simplify: 180n−360=144n⇒36n=360⇒n=10.
n=10
Verify the result
Check: interior angle =10(10−2)×180=108×180=144°, which matches the given value.
108×180=144°
B is correct because solving \frac{(n-2)\times180°{n}=144° yields n=10
Remember that the exterior angles of any polygon sum to 360°, which provides a quick way to find the number of sides when an interior angle is known.