If the interior angle is `144^@` more than exterior angle of regular polygon, then what will be the number of sides of polygon?

Options

A. 10
B. 8
C. 20
D. 15

Answer

To find the number of sides of a regular polygon given that its interior angle is `144°` more than its exterior angle, we can follow these steps:

### Step 1: Define the angles
Let the exterior angle be denoted as \( x \) and the interior angle as \( y \).

### Step 2: Establish the relationship between interior and exterior angles
We know that the sum of the interior and exterior angles of a polygon is always \( 180° \):
\[ x + y = 180° \]
From this, we can express the interior angle in terms of the exterior angle:
\[ y = 180° - x \]

### Step 3: Use the given information
According to the problem, the interior angle is \( 144° \) more than the exterior angle:
\[ y = x + 144° \]

### Step 4: Set up the equations
Now we have two equations:
1. \( y = 180° - x \)
2. \( y = x + 144° \)

### Step 5: Substitute the second equation into the first
Substituting \( y \) from the second equation into the first gives:
\[ x + 144° = 180° - x \]

### Step 6: Solve for \( x \)
Now, we can solve for \( x \):
\[ x + x = 180° - 144° \]
\[ 2x = 36° \]
\[ x = 18° \]

### Step 7: Find the number of sides
The exterior angle \( x \) can be used to find the number of sides \( n \) of the polygon using the formula:
\[ n = \frac{360°}{x} \]
Substituting \( x = 18° \):
\[ n = \frac{360°}{18°} = 20 \]

### Conclusion
Thus, the number of sides of the polygon is \( 20 \).

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