The sum of all interior angles of a regular convex polygon is `1440^(@)`. The measure of each of its interior angles is

Options

A. `72^(@)`
B. `108^(@)`
C. `144^(@)`
D. `150^(@)`

Answer

To find the measure of each interior angle of a regular convex polygon given that the sum of all interior angles is \(1440^\circ\), we can follow these steps:

### Step 1: Use the formula for the sum of interior angles
The formula for the sum of the interior angles of a polygon with \(n\) sides is given by:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
Given that the sum of the interior angles is \(1440^\circ\), we can set up the equation:
\[ (n - 2) \times 180 = 1440 \]

### Step 2: Solve for \(n\)
To find \(n\), we first divide both sides of the equation by \(180\):
\[ n - 2 = \frac{1440}{180} \]
Calculating the right side:
\[ n - 2 = 8 \]
Now, add \(2\) to both sides:
\[ n = 8 + 2 = 10 \]

### Step 3: Find the measure of each interior angle
Now that we know the polygon has \(10\) sides, we can find the measure of each interior angle using the formula:
\[ \text{Each interior angle} = \frac{\text{Sum of interior angles}}{n} \]
Substituting the known values:
\[ \text{Each interior angle} = \frac{1440}{10} = 144^\circ \]

### Final Answer
The measure of each interior angle of the polygon is \(144^\circ\).

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