Question

4. How many sides does a regular polygon have if each of its interior angles
is 165°?
​

Answer 1

Answer:

24

Step-by-step explanation:

the regular polygon with interior angle each measuring 165 degrees is a 24-sided polygon.

Answer 2

Answer:

☞Given:

• How many sides does a regular polygon have if each of its interior angles is 165°

☞To Find:

• sides of a regular polygon

☞Solution:

the sum S of interior angle measure of a polygon with 'n' sides is

$s = (n - 2)180 {}^{o}$

The measure of each interior angle the regular polygon is

$\frac{s}{n}$

Divide the sum of interior angles measures by'n'

Since the measure of each interior angle the regular polygon is 165°

$\frac{(n - 2) 180}{n} = 165 \: \: \: \: \: \: \: \: \: \: \: \: \: substitude$

$(n - 2)180 = 165 \: \: \: \: \: \: \: \: \: cross \: products \: property$

$180n - 360 = 165n \: \: \: \: \: \: \: use \: distributive \: property$

$180n - 360 + 360 = 165n + 360 \: \: \: \: \: \: \: \: \: add \: 360 \: to \: both \: sides$

$180n = 165n + 360 \: \: \: \: \: \: \: simplify$

$180n - 165n = 165n - 165n + 360 \: \: \: subtract \: 165n \: both \: sides \:$

$\frac{15n}{15} = \frac{360}{15} \: \: \: \: divide \: both \: sides \: by \: 15$

$n = 24$

✧✧The polygon has 24 Sides✧✧