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3 years ago

Find measures of each exterior angle of a regular polygon with 16 sides

Mathematics

2 answers:

Maksim231197 [3]3 years ago

3 0

The measure of each exterior angle = the measure of each central angle.
each angle = 360 / 16 = 22.5

qwelly [4]3 years ago

3 0

Answer: 22.5°

Step-by-step explanation: In this problem, we are asked to find the measure of each exterior angle of a regular polygon that has 16 sides.

The formula for finding the measure of each exterior angle of a regular polygon is similar to the formula for finding the measure of each interior angle.

We take the sum of the measures of the exterior angles which is always 360° divided by the number of sides in the polygon which is n. So the formula for finding the measure of each exterior angle of a regular polygon is 360/n.

In this problem, since the polygon has 16 sides, we simply plug a 16 in for n in our formula and we have 360 divided by 16 which is 22.5.

So the measure of each exterior angle of a regular polygon that has 16 sides is 22.5°.

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Answer:

The solutions of the original equation are x=-5 and x=-2

Step-by-step explanation:

we have

$(x+3)^2+(x+3)-2=0$

Let

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$(u)^2+(u)-2=0$

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Alternative Method

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$(u)^2+(u)-2=0$

$a=1\\b=1\\c=-2$

substitute in the formula

$u=\frac{-1\pm\sqrt{1^{2}-4(1)(-2)}} {2(1)}$

$u=\frac{-1\pm\sqrt{9}} {2}$

$u=\frac{-1\pm3} {2}$

$u=\frac{-1+3} {2}=1$

$u=\frac{-1-3} {2}=-2$

the solutions are

u=-2,u=1

Find the solutions of the original equation

For u=-2

$-2=(x+3)$ ----> $x=-2-3=-5$

For u=1

$1=(x+3)$ ----> $x=1-3=-2$

therefore

The solutions of the original equation are

x=-5 and x=-2

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