Question

What is the sum of the interior angle measures in a \[35\]-gon?

Answer 1

Hint: In this question ,we have to find out the sum of the interior angle measures in the given polygon.
First, we need to find the number of sides in the polygon and then we need to apply the formula to find out the required result.
Formula:
The sum of the interior angles = \[\left( {n - 2} \right) \times {180^\circ }\]
where, n is the number of sides of the polygon.

Complete step-by-step solution:
We need to find out the sum of the interior angle measures in a \[35\]-gon.
Now, if we draw in all of the diagonals from one vertex to all the other vertices, we can form triangles.
The number of triangles will always be \[2\] less than the number of sides.
If there are \[3\] sides → \[1\Delta \]
If there are \[4\] sides → \[2\Delta \]
If there are \[5\] sides → \[3\Delta \]
If there are \[10\] sides → \[8\Delta \]
If there are \[20\] sides → \[18\Delta \]
If there are \[35\] sides → \[33\Delta \]
Each triangle has \[{180^\circ }\] and this will give the sum of the angles in the polygon.
\[33 \times {180^\circ } = {5940^\circ }\]
That is why the formula to find the sum of the angles in a polygon is:
\[\left( {n - 2} \right) \times {180^\circ }\]
Hence, the sum of the interior angle measures in a \[35\]-gon is \[{5940^\circ }\].

Note: In geometry, a polygon is a plane figure that is described by a finite number of straight-line segments connected to form a closed polygonal chain or polygonal circuit. The solid plane region, the bounding circuit, or the two together, may be called a polygon.
For example, a hexagon is a polygon with side six.