Question

NO LINKS!! URGENT HELP PLEASE!!​

Answer 1

a. Find the sum of the interior angles of a decagon.

`\sf {\text{To find the sum of the interior angles of a polygon, we can use the formula:}} \\`

`\sf S = (n - 2) * 180^\circ \\`

`\sf \text{For a decagon (10 sides), the sum of the interior angles can be calculated as follows:} \\`

`\sf S = (10 - 2) * 180^\circ \\`

`\sf S = 8 * 180^\circ \\`

`\sf S = 1440^\circ \\`

c. If the sum of the interior angles of a regular polygon is 10,800°, how many sides does the polygon have?

`\sf \text{Using the same formula as before,} \\`

`\sf S = (n - 2) * 180^\circ \\`

`\sf \text{we can solve for n, the number of sides.} \\`

`\sf 10,800^\circ = (n - 2) * 180^\circ \\`

`\sf (10,800^\circ)/(180^\circ) = n - 2 \\`

`\sf 60 = n - 2 \\`

`\sf n = 60 + 2 \\`

`\sf n = 62 \\`

`\sf \text{Therefore, the polygon has 62 sides.} \\`

e. What is the exterior angle of a regular 90-gon?

`\sf \text{To find the measure of each exterior angle of a regular polygon, we can use the formula:} \\`

`\sf \text{Each exterior angle } = (360^\circ)/(n) \\`

`\sf \text{where n represents the number of sides of the polygon.} \\`

`\sf \text{For a regular 90-gon (90 sides), we can calculate the measure of each exterior angle as follows:}`

`\sf \text{Each exterior angle } = (360^\circ)/(90) \\`

`\sf \text{Each exterior angle } = 4^\circ \\`

`\sf \text{Therefore, the exterior angle of a regular 90-gon measures } 4^\circ. \\`