$A$ regular polygon has $170$ diagonals. Then the measure of the interior angle of the polygon is

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

$A$ polygon has $54$ diagonals. Then,the number of its sides is

Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of lines in $\mathbb{R}^2$ passing through $(0,0)$ and exactly one other point in $S$ is:

Let $ABC$ be a triangle. Consider four points $p_1, p_2, p_3, p_4$ on the side $AB$,five points $p_5, p_6, p_7, p_8, p_9$ on the side $BC$,and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side $AC$. None of these points is a vertex of the triangle $ABC$. The total number of pentagons that can be formed by taking all the vertices from the points $p_1, p_2, \ldots, p_{13}$ is . . . . . . .

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to