Question
Determine the sum of the interior angles of a polygon with 19 sides
1. In right angles
2. In degrees
1. In right angles
2. In degrees
Answers
GPT-4o mini
To determine the sum of the interior angles of a polygon, you can use the formula:
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon.
For a polygon with 19 sides:
1. **Sum in degrees**:
\[
\text{Sum of interior angles} = (19 - 2) \times 180^\circ = 17 \times 180^\circ = 3060^\circ
\]
2. **Sum in right angles**:
Since \( 1 \text{ right angle} = 90^\circ \), we can convert the sum in degrees to right angles by dividing by 90:
\[
\text{Sum in right angles} = \frac{3060^\circ}{90^\circ} = 34
\]
Thus, the answers are:
1. The sum of the interior angles in degrees: **3060 degrees**
2. The sum of the interior angles in right angles: **34 right angles**
\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon.
For a polygon with 19 sides:
1. **Sum in degrees**:
\[
\text{Sum of interior angles} = (19 - 2) \times 180^\circ = 17 \times 180^\circ = 3060^\circ
\]
2. **Sum in right angles**:
Since \( 1 \text{ right angle} = 90^\circ \), we can convert the sum in degrees to right angles by dividing by 90:
\[
\text{Sum in right angles} = \frac{3060^\circ}{90^\circ} = 34
\]
Thus, the answers are:
1. The sum of the interior angles in degrees: **3060 degrees**
2. The sum of the interior angles in right angles: **34 right angles**