Answer :
To find the measure of one interior angle of a regular 14-gon, follow these steps:
1. Understand the formula: The measure of an interior angle of a regular polygon can be determined using the formula:
[tex]\[ \text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n} \][/tex]
where \( n \) is the number of sides of the polygon.
2. Substitute the value of \( n \): For a 14-gon, \( n = 14 \).
[tex]\[ \text{Interior angle} = \frac{(14 - 2) \times 180^\circ}{14} \][/tex]
3. Simplify within the parentheses:
[tex]\[ 14 - 2 = 12 \][/tex]
4. Multiply by 180 degrees:
[tex]\[ 12 \times 180^\circ = 2160^\circ \][/tex]
5. Divide by 14:
[tex]\[ \frac{2160^\circ}{14} \approx 154.2857^\circ \][/tex]
Therefore, the measure of one interior angle of a regular 14-gon is approximately \( 154.2857^\circ \).
Among the given options:
A. 154.3
B. 150
C. 160
D. 140
The closest value to our calculated measure is A. 154.3.
1. Understand the formula: The measure of an interior angle of a regular polygon can be determined using the formula:
[tex]\[ \text{Interior angle} = \frac{(n - 2) \times 180^\circ}{n} \][/tex]
where \( n \) is the number of sides of the polygon.
2. Substitute the value of \( n \): For a 14-gon, \( n = 14 \).
[tex]\[ \text{Interior angle} = \frac{(14 - 2) \times 180^\circ}{14} \][/tex]
3. Simplify within the parentheses:
[tex]\[ 14 - 2 = 12 \][/tex]
4. Multiply by 180 degrees:
[tex]\[ 12 \times 180^\circ = 2160^\circ \][/tex]
5. Divide by 14:
[tex]\[ \frac{2160^\circ}{14} \approx 154.2857^\circ \][/tex]
Therefore, the measure of one interior angle of a regular 14-gon is approximately \( 154.2857^\circ \).
Among the given options:
A. 154.3
B. 150
C. 160
D. 140
The closest value to our calculated measure is A. 154.3.
