Find the measure of each angle (in degrees) of a regular octagon. (a) 90° (b) 60° (c) 135° (d) 145°

To solve for the measure of each interior angle of a regular octagon, we follow these steps:

1. **Formula for the sum of interior angles**:
The sum of the interior angles of any polygon can be calculated using the formula:
\[
S = (n - 2) \times 180^\circ
\]
where \( n \) is the number of sides of the polygon.

2. **Calculate the sum of the interior angles of an octagon**:
For a regular octagon, \( n = 8 \). Substituting into the formula:
\[
S = (8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ
\]

3. **Measure of each interior angle**:
In a regular polygon, all interior angles are equal. The measure of each interior angle is:
\[
\text{Each angle} = \frac{S}{n} = \frac{1080^\circ}{8} = 135^\circ
\]

4. **Answer**:
The measure of each interior angle of a regular octagon is \( \mathbf{135^\circ} \).
Therefore, the correct answer is:
\[
\text{(c) } 135^\circ
\]

Plain text version:
To solve for the measure of each interior angle of a regular octagon:
1. Use the formula for the sum of interior angles: S = (n - 2) * 180°, where n is the number of sides.
2. For an octagon, n = 8. So, S = (8 - 2) * 180° = 6 * 180° = 1080°.
3. In a regular polygon, each angle = S / n. Therefore, each angle = 1080° / 8 = 135°.
Answer: (c) 135°.