Exterior angles of angular polygon are in the ratio of 2:3. a) Find the size of the exterior angle. b) What is the interior angle sum of the hexagon?

We assume the ratio of the exterior angle to the interior angle is $2:3$.

Alternatively, $E = \frac{2}{3}I = \frac{2}{3}(108^\circ) = 72^\circ$.
The exterior angle is $\boxed{72^\circ}$.
(This corresponds to a regular pentagon, as $360^\circ / 72^\circ = 5$ sides).

b) What is the interior angle sum of a heptagon?

A heptagon has $n=7$ sides.

The sum of interior angles of an $n$-sided polygon is given by:

The interior angle sum of a heptagon is $\boxed{900^\circ}$.

7) Find the value of x in the figures below.

a) The figure is a quadrilateral. The sum of the interior angles of a quadrilateral is $360^\circ$.
The angles are $(x-5)^\circ$, $(x-1)^\circ$, $(x+11)^\circ$, and $(x+19)^\circ$.

The value of $x$ is $\boxed{84}$.

b) The figure is a 5-pointed star (pentagram). The sum of the angles at the points of a pentagram is $180^\circ$.
All five angles are given as $x$.

The value of $x$ is $\boxed{36}$.

c) The figure is a rectangle. In a rectangle, opposite sides are equal in length.
The left side is $2x$ and the right side is $x+1$.

The value of $x$ is $\boxed{1}$.

d) The figure shows two angles on a straight line. Angles on a straight line sum to $180^\circ$.
The angles are $x$ and $2x$.

The value of $x$ is $\boxed{60}$.

e) The figure is a hexagon. The sum of the interior angles of an $n$-sided polygon is $(n-2) \times 180^\circ$.
For a hexagon, $n=6$.
The angles are $(x+9)^\circ$, $(x-1)^\circ$, $(x+1)^\circ$, $(x+3)^\circ$, $(x+5)^\circ$, and $(x+7)^\circ$.

The value of $x$ is $\boxed{116}$.

f) The figure shows three angles around a point. Angles around a point sum to $360^\circ$.
The angles are $x$, $110^\circ$, and $150^\circ$.

The value of $x$ is $\boxed{100}$.