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3 years ago

Es The measure of an interior angle of a regular polygon is 120°. What is the measurb of each exterior angle? The polygon has

Mathematics

1 answer:

Troyanec [42]3 years ago

5 0

The measure of each exterior angle is 60° and the polygon has 6 sides ⇒ 4th answer

Step-by-step explanation:

In a regular n-side polygon:

All sides are equal in lengths
All angles are equal in measure
The measure of each interior angle = $\frac{(n-2)*180}{n}$
The measure of each exterior angle = $\frac{360}{n}$
The sum of interior angle and exterior angle at a vertex is 180°

∵ The measure of an interior angle of a regular polygon is 120°

∵ The sum of interior angle and exterior angle at a vertex = 180°

∴ The measure of each exterior angle = 180 - 120

∴ The measure of each exterior angle = 60°

∵ The measure of each exterior angle = $\frac{360}{n}$

- Substitute the measure of the exterior angle by 60

∴ $60=\frac{360}{n}$

- By using cross multiplication

∴ 60 n = 360

- Divide both sides by 60

∴ n = 6

∴ The polygon has 6 sides

The measure of each exterior angle is 60° and the polygon has 6 sides

Learn more:

You can learn more about polygons in brainly.com/question/6281564

#LearnwithBrainly

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4 years ago

The cost of 1 m ribbon is ₹ 75. Find the cost of 7/5 metres of ribbon

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Given that

The cost of 1 m ribbon = Rs.75

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3 years ago

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3 years ago

Read 2 more answers

Keenan will run 2.5 miles from his house to Jared’s house. He plans to hang out for 45 minutes before walking home. If he can ru

jenyasd209 [6]

Answer:

Kennan will be from home approximately an hour and 48 minutes.

Step-by-step explanation:

We must know that total time ( $t_{T}$ ) that Keenan will be from home is the sum of run ( $t_{R}$ ), hang out ( $t_{H}$ ) and walk times ( $t_{W}$ ), measured in hours:

$t_{T} = t_{R}+t_{H}+t_{W}$

If Keenan runs and walks at constant speed, then equation above can be expanded:

$t_{T} = \frac{x_{R}}{v_{R}}+t_{H}+ \frac{x_{W}}{v_{W}}$

Where:

$x_{R}$ , $x_{W}$ - Run and walk distances, measured in miles.

$v_{R}$ , $v_{W}$ - Run and walk speeds, measured in miles per hour.

Given that $x_{R}=x_{W} = 2.5\,mi$ , $v_{R} = 6\,\frac{mi}{h}$ , $v_{W} = 4\,\frac{mi}{h}$ and $t_{H} = 0.75\,h$ , the total time is:

$t_{T} = \frac{2.5\,mi}{6\,\frac{mi}{h} } + 0.75\,h+\frac{2.5\,mi}{4\,\frac{mi}{h} }$

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3 years ago

Domain and Range for the function f(x)=5IXI is

shutvik [7]

Answer:

The domain of the function f(x) is:

$\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

The range of the function f(x) is:

$\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}$

Step-by-step explanation:

Given the function

$f\left(x\right)=5\left|x\right|$

Determining the domain:

We know that the domain of the function is the set of input or arguments for which the function is real and defined.

In other words,

Domain refers to all the possible sets of input values on the x-axis.

It is clear that the function has undefined points nor domain constraints.

Thus, the domain of the function f(x) is:

$\mathrm{Domain\:of\:}\:5\left|x\right|\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Determining the range:

We also know that range is the set of values of the dependent variable for which a function is defined.

In other words,

Range refers to all the possible sets of output values on the y-axis.

We know that the range of an Absolute function is of the form

$c|ax+b|+k\:\mathrm{is}\:\:f\left(x\right)\ge \:k$

$k=0$

Thus, the range of the function f(x) is:

$\mathrm{Range\:of\:}5\left|x\right|:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)\ge \:0\:\\ \:\mathrm{Interval\:Notation:}&\:[0,\:\infty \:)\end{bmatrix}$

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