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.

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**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:
$$
D = 2 \times 6.4\text{ cm} = 12.8\text{ cm}.
$$
a) A convex octagon has 20 diagonals. b) The sum of the angles in a convex octagon is 1080 degrees. c) In a regular octagon, each angle measures 135 degrees. d) If the radius of a circle is 6.4 cm, then the diameter is 12.8 cm.

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