If the sum of the interior angles of a regular polygon is , what is the size of each interior angle?

Ask by Ortiz Little. in Australia

Nov 01,2024

Question

If the sum of the interior angles of a regular polygon is $$ 2880^{\circ} $$, what is the size of each interior angle? $$ 156^{\circ} $$ $$ 160^{\circ} $$ $$ 165^{\circ} $$ $$ 150^{\circ} $$

UpStudy AI · Accepted Answer

To find the size of each interior angle of a regular polygon given that the sum of the interior angles is $$ 2880^{\circ} $$, we can use the formula for the sum of the interior angles of a polygon:

$$
S = (n - 2) \times 180^{\circ}
$$

where $$ S $$ is the sum of the interior angles and $$ n $$ is the number of sides of the polygon.

Setting $$ S = 2880^{\circ} $$, we have:

$$
2880 = (n - 2) \times 180
$$

To solve for $$ n $$, we first divide both sides by $$ 180 $$:

$$
\frac{2880}{180} = n - 2
$$

Calculating the left side:

$$
\frac{2880}{180} = 16
$$

Thus, we have:

$$
16 = n - 2
$$

Adding $$ 2 $$ to both sides gives:

$$
n = 18
$$

Now that we know the polygon has $$ 18 $$ sides, we can find the size of each interior angle using the formula for the interior angle of a regular polygon:

$$
\text{Interior angle} = \frac{S}{n}
$$

Substituting the values we have:

$$
\text{Interior angle} = \frac{2880}{18}
$$

Calculating this gives:

$$
\text{Interior angle} = 160^{\circ}
$$

Thus, the size of each interior angle is

$$
\boxed{160^{\circ}}
$$
The size of each interior angle is $$ 160^{\circ} $$.

If the sum of the interior angles of a regular polygon is , what is the size of each interior angle?

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