Final answer:
The base angle of an octagon is 135° and its central angle is 45°. For a 35-gon, the base angle is approximately 169.714° and the central angle is approximately 10.286°.
Step-by-step explanation:
To calculate the central angle and base angle of an octagon and a 35-gon, we can use the fact that the sum of the interior angles of a polygon with n sides is given by the formula (n - 2) × 180°. For an octagon, which has 8 sides, the sum of the interior angles is (8 - 2) × 180° = 6 × 180° = 1080°. Dividing by the number of angles, which is also the number of sides, gives us the measure of each interior (or base) angle: 1080° / 8 = 135°. To find the central angle of an octagon, we divide 360° by the number of sides, which gives 360° / 8 = 45°.
Similarly, for a 35-gon, the sum of the interior angles is (35 - 2) × 180° = 33 × 180° = 5940°. Each interior angle of a 35-gon would then be 5940° / 35 = 169.714°. The central angle of a 35-gon can be found by dividing the full circle 360° by the number of sides, giving us 360° / 35 ≈ 10.286°.