To find the measure of one interior angle of a regular octagon, 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 an octagon, \( n = 8 \).
Substituting \( n \) into the formula:
\[ \text{Interior Angle} = \frac{(8 - 2) \times 180^\circ}{8} = \frac{6 \times 180^\circ}{8} \]
Calculating this step-by-step:
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Calculate \( 6 \times 180^\circ \): \[ 6 \times 180^\circ = 1080^\circ \]
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Divide by 8: \[ \frac{1080^\circ}{8} = 135^\circ \]
Therefore, the measure of one interior angle of a regular octagon is \( \boxed{135^\circ} \).
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