a$.$ Using complete induction, prove that the sum of the angles of a convex polygon with

$$

N edges, for

$$

$>=$

$3$

N$>=3,$ is

$($

$$

$$

$2$

$)$

$\backslash$times

$180$

$($N$2)\backslash$times $180.$

A convex polygon is a closed two$-$dimensional geometric shape with straight lines that meet at their endpoints. A convex polygon has angles that are all less than $180$ degrees.

b$.$ Using structural induction, prove that any regular binary tree has an odd number of nodes, where a regular binary tree is a binary tree whose internal nodes have exactly two subtrees