Question

Find the sum of the measures of the interior angles of each of the following convex polygons: a pentagon, an octagon, a dodecagon, a 40-gon, a 52-gon, a 100-gon.

Answer 1

The sum of the measures of the interior angles of convex polygons can be calculated using (n-2) times 180, where n is the number of sides of the polygon.

Step-by-step explanation:

In a convex polygon, the sum of the measures of the interior angles equals (n-2) times 180 degrees, where n is the number of sides of the polygon.

For a pentagon with 5 sides, the sum of its interior angles is (5-2) × 180 = 540 degrees.

For an octagon with 8 sides, the sum of its interior angles is (8-2) × 180 = 1080 degrees.

For a dodecagon with 12 sides, the sum of its interior angles is (12-2) × 180 = 1800 degrees.

Similarly, for a 40-gon, the sum of its interior angles is (40-2) × 180 = 6840 degrees.

For a 52-gon, the sum of its interior angles is (52-2) × 180 = 9000 degrees.

For a 100-gon, the sum of its interior angles is (100-2) × 180 = 17640 degrees.

Answer 2

`540^(\circ),\ 1080^(\circ),\ 1800^(\circ),\ 6840^(\circ),\ 9000^(\circ),\ 17640^(\circ)`

Step-by-step explanation:

The sum of the measures of the interior angles of each convex n-sided polygon is always equal to

`(n-2)\cdot 180^(\circ).`

1. A pentagon is 5-sided polygon, then the sum of the measures of the interior angles of pentagon is

`(5-2)\cdot 180^(\circ)=540^(\circ).`

2. An octagon is 8-sided polygon, then the sum of the measures of the interior angles of octagon is

`(8-2)\cdot 180^(\circ)=1080^(\circ).`

3. A dodecagon is 12-sided polygon, then the sum of the measures of the interior angles of dodecagon is

`(12-2)\cdot 180^(\circ)=1800^(\circ).`

4. For 40-sided polygon the sum of the measures of the interior angles is

`(40-2)\cdot 180^(\circ)=6840^(\circ).`

5. For 52-sided polygon the sum of the measures of the interior angles is

`(52-2)\cdot 180^(\circ)=9000^(\circ).`

6. For 100-sided polygon the sum of the measures of the interior angles is

`(100-2)\cdot 180^(\circ)=17640^(\circ).`