Question

If the sum of the interior angles of a polygon is 720°, what type of polygon is it?

Answer 1

Please read the explanation.

Explanation:

Given:

Sum of the interior angles of a polygon is: `color(blue)(720^@`

The relationship between the number of sides of a polygon and the sum of interior angles is `color(blue)(180^@*(n-2)`,

where `color(blue)(n` is the number of sides of the polygon.

Hence, we have

`color(blue)(180^@*(n-2)=720^@`

Divide both sides of the equation by `color(red)(180^@`

`color(blue)[[180^@*(n-2)]/color(red)(180^@]=720^@/color(red)(180^@`

`color(blue)[[cancel 180^@*(n-2)]/color(red)(cancel 180^@]=720^@/color(red)(180^@`

`rArr (n-2) = 4`

Add `color(red)2` to both sides of the equation.

`rArr (n-2)+color(red)2 = 4+color(red)2`

`rArr (n-cancel 2)+color(red)cancel 2 = 4+color(red)2`

`rArr n=6`

Hence, the required polygon must have 6 sides.

A Hexagon is a six-sided polygon.

Hence, the type of polygon required is a Hexagon.

If you are interested, you can find an image of a regular hexagon below:

Hope it helps.