Question

solve for the missing angles in this rectangle.1 Int just means 1 interior 1 Ent just means 1 exterior.

Answer 1

Given a table of polygons

For the first row,

Given that the 1 exterior angle of the polygon is given, to find the number of sides, n, the formula is

`\begin{gathered} \text{One exterior angle}=(360\degree)/(n) \\ 120\degree=(360\degree)/(n) \\ \text{Crossmultiply} \\ 120\degree* n=360\degree \\ \text{Divide both sides by 120} \\ n=(360\degree)/(120\degree) \\ n=3 \end{gathered}`

The number of sides, n, of the polygon is three, thus it is a triangle.

A regular triangle has

`\begin{gathered} 3\text{ sides} \\ Sum\text{ of interior angles is 180}\degree \\ One\text{ interior angle is 60}\degree \\ Sum\text{ of exterior angles is 360}\degree \\ \text{One exterior angle is 120}\degree \end{gathered}`

For the second row

Given that sum of the interior angles of the polygon is 720°, to find the number of sides of the polygon,

Using the formula to find the sum of the interior angles of a polygon which is

`\begin{gathered} Sum\text{ of interior angles}=(n-2)180\degree \\ 720\degree=(n-2)180\degree \\ \text{Divide both sides by 180}\degree \\ (720\degree)/(180\degree)=((n-2)180\degree)/(180\degree) \\ 4=n-2 \\ \text{Collect like terms} \\ n=4+2 \\ n=6\text{ sides} \end{gathered}`

Since the number of sides is 6, thus, it is a hexagon.

For a regular hexagon, is tas

`\begin{gathered} 6\text{ sides} \\ \text{Sum of interior angles is 720}\degree \\ One\text{ interior angle is }120\degree \\ \text{Sum of exterior angles is 360}\degree \\ \text{One exterior angle is 60}\degree \end{gathered}`

The table is shown below