2. Numerical completion: \( \qquad \) a) A convex octagon has \( \qquad \) diagonals. \( \qquad \) b) The sum of the angles in a convex octagon is \( \qquad \) degrees. \( \qquad \) c) In a regular octagon, each angle measures \( \qquad \) degrees. \( \qquad \) d) If the radius of a circle is 6.4 cm , then the diameter is \( \qquad \) cm.

**a) Diagonals in a convex octagon** A convex polygon with \( n \) sides has \[ \frac{n(n-3)}{2} \] diagonals. For an octagon (\( n = 8 \)): \[ \frac{8(8-3)}{2} = \frac{8 \times 5}{2} = \frac{40}{2} = 20. \] Thus, there are \( 20 \) diagonals. **b) Sum of the angles in a convex octagon** The sum \( S \) of interior angles in a convex polygon with \( n \) sides is given by: \[ S = (n-2) \times 180^\circ. \] For an octagon: \[ S = (8-2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ. \] **c) Measure of each angle in a regular octagon** In a regular octagon, each interior angle \( A \) is: \[ A = \frac{S}{n} = \frac{1080^\circ}{8} = 135^\circ. \] **d) Diameter of a circle with radius 6.4 cm** The diameter \( D \) is twice the radius: \[ D = 2 \times 6.4\text{ cm} = 12.8\text{ cm}. \]