Question

A regular dodecagon is a two-dimensional figure with 12 sides.

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What is the measure of one angle in a dodecagon?


150º


165º


1800º


1980º

Answer 1

To find the measure of one interior angle in a regular dodecagon, we can use the formula for the measure of an interior angle of a regular polygon, which is given by:

\[
\text{Interior Angle} = \frac{(n - 2) \times 180^\circ}{n}
\]

where \( n \) is the number of sides of the polygon. For a dodecagon, \( n = 12 \).

Substituting \( n \) into the formula:

\[
\text{Interior Angle} = \frac{(12 - 2) \times 180^\circ}{12}
\]

This simplifies to:

\[
\text{Interior Angle} = \frac{10 \times 180^\circ}{12}
\]

Calculating the right-hand side:

\[
\text{Interior Angle} = \frac{1800^\circ}{12} = 150^\circ
\]

Therefore, the measure of one angle in a regular dodecagon is \( 150^\circ \).

So the correct option is:

**150º**