All categories

7 days ago

Given the regular polygon, what is the measure of each numbered angle? :)

Mathematics

2 answers:

Inessa [9K]7 days ago

5 0

Response:

The right choice is option C.

Explanation in detail:

We were presented with an illustration of a regular polygon and tasked with determining the measure of each numbered angle.

Initially, we need to calculate the measure of every interior angle of the given polygon using the formula:

$\text{Each interior angle}=\frac{180(n-2)}{n}$ , where n denotes the number of sides of the regular polygon.

Given that our polygon is regular and has 10 sides, the measurement for each interior angle will equal:

$\text{Each interior angle}=\frac{180(10-2)}{10}$

$\text{Each interior angle}=18(8)$

$\text{Each interior angle}=144$

Since the interior angle of our decagon splits into two sections, the measures for angle 2 and the unnamed angle will be half of 144 degrees.

$m\angle 2=\frac{144^{\circ}}{2}$

$m\angle 2=72^{\circ}$

Thus, angle 2 measures 72 degrees.

According to the angle sum property, all triangle angles total 180 degrees, enabling us to determine the measurement of angle 1 as:

$m\angle 1+m\angle 2+\text{Measure of unnumbered angle}=180^{\circ}$

$m\angle 1+72^{\circ}+72^{\circ}=180^{\circ}$

$m\angle 1+144^{\circ}=180^{\circ}$

$m\angle 1+144^{\circ}-144^{\circ}=180^{\circ}-144^{\circ}$

$m\angle 1=36^{\circ}$

Therefore, angle 1 is 36 degrees.

Reviewing the available choices confirms that option C is indeed correct.

PIT_PIT [9.1K]7 days ago

4 0

It should be the third option
72+72= 144 and subsequently 144+72=180 degrees

You might be interested in

As part of Kayla's exercise program, she either runs 6 miles/day or rides her bike 10 miles/day. Her new goal is to cover a mini

lawyer [9240]

To find out the number of days, we should create equations based on the values provided. The total distance Kayla aims to travel combines both her running distance and her biking distance.

200 miles = (6 miles/day)x + (10 miles/day)y

where x signifies the days she spent running and y represents the days bike riding.

If the minimum biking days are set to be 15, indicated by y = 15, we have:

200 miles = (6 miles/day)x + (10 miles/day)(15 days)

Solving for x gives:
200 = 6x + 150
50 = 6x
x = 8.3333 days

Total days = 15 days biking + 8.3333 days running = 23.3333 days, approximately making it 24 days.

8 0

1 month ago

Read 2 more answers

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

zzz [9080]

Answer:

Based on the findings, we infer that the average cost of a wedding is lower than the $30,000 that was initially suggested.

Step-by-step explanation:

The following data set is provided: (in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ denotes data points, $\bar{x}$ represents the mean, and n indicates the number of samples.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{236100}{8} = 29512.5$

The sum of squares of the differences equals 3408750

$S.D = \sqrt{\frac{3408750}{7}} = 697.82$

The population mean, μ = $30,000

The sample mean, $\bar{x}$ = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $697.82

Initially, we formulate the null hypothesis and the alternative hypothesis.

$H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}$ A one-tailed t-test will be conducted for this analysis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

$t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975$

<pnow>

$t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894$

$t_{stat} < t_{critical}$

Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.

</pwe></pgiven></pnow></pinserting>

8 0

21 day ago

On a baseball field, the pitcher’s mound is 60.5 feet from home plate. During practice, a batter hits a ball 195 feet at an angl

tester [8842]

For this scenario, we can visualize that all points form a triangle. The three vertices are at the pitcher's mound, home plate, and the location where the outfielder catches the ball. We know two sides of the triangle and the angle that lies between these two sides.

<span>Using the cosine law, we can find the unknown third side. The formula to apply is:</span>

c^2 = a^2 + b^2 - 2ab cos θ

Where:

a = 60.5 ft

b = 195 ft

θ = 32°

Substituting the provided values results in:

c^2 = (60.5)^2 + (195)^2 - 2(60.5)(195) cos(32)

c^2 = 3660.25 + 38025 - 20009.7

c^2 = 21,675.56

c = 147.23 ft

<span>Thus, the distance the outfielder throws the ball towards home plate is approximately 147.23 ft.</span>

8 0

22 days ago

Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $20dollar out of his present on bo

Svet_ta [9500]

To create a recursive formula, start by identifying if the sequence is geometric (for example, if the same number is being multiplied or divided for one term or more). After that, determine the common ratio (the specific number used for multiplication or division).

3 0

8 days ago

Read 2 more answers

Bhavik bought 333 liters of milk and 555 loaves of bread for a total of \$11$11dollar sign, 11. A month later, he bought 444 lit

Leona [9271]

Assuming the cost of 1 liter of milk is x$

and the cost of 1 loaf of bread is y$

Based on the information provided

the equations are 333x + 555y = 11

and 444x + 444y = 10

By subtracting these expressions,

we derive

(333x + 555y = 11) * 444

(444x + 444y = 10) * 333

(-) (-) (-)

147852x + 246420y = 4884

147852x + 147852y = 3330

(-) (-) (-)

------------------------------

98568y = 1554

y = 1554/98568

= 0.0157$

= 0.02$

Cost of 1 loaf of bread is 2 cents

Substituting the value of y back in

333x + 555*0.0157 = 11333x + 8.7135 = 11333x = 2.2865x = 2.2865/333x = 0.00068$ = 0.01$

Cost of 1 liter of milk = 1 cent

1.5

6 0

13 hours ago