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2 years ago

One of the interior angles of a regular polygon is 144. fine the number of sides of the polygon

Mathematics

2 answers:

lora16 [44]2 years ago

3 0

Answer:

Step-by-step explanation:

In any polygon

exterior angle + interior angle = 180° , thus

exterior angle + 144 = 180 ( subtract 144 from both sides )

exterior angle = 36°

The sum of the exterior angles = 360°

Thus number of sides n is calculated as

n = 360 ÷ 36 = 10

navik [9.2K]2 years ago

3 0

Answer:

<h2>The polygon has 10 sides</h2>

Step-by-step explanation:

One of the interior angles of a polygon can be found using the formula

<h3> $\frac{(n - 2) \times180\degree }{n}$ </h3>

where n is the number of sides of the polygon

From the question

One of the interior angles = 144

To find the number of sides substitute this value into the above formula and solve for n

That's

<h3> $144 = \frac{(n - 2) \times 180}{n}$ </h3>

<u>Cross multiply</u>

We have

<h3> $144n = (n - 2) \times 180$ </h3>

<u>Expand the terms in the bracket</u>

<u>Group like terms</u>

<u>Divide</u><u> </u><u>both</u><u> sides</u><u> by</u><u> </u><u> </u><u>-</u><u> </u><u>3</u><u>6</u>

That's

We have the final answer as

<h3>n = 10 sides </h3>

Hope this helps you

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How do I solve this, and what is the answer? please and thank you.

vovangra [49]

Answer:

A. (x +8) + (-4x+31)/(x^2+2x+1)

Step-by-step explanation:

When you perform long division of polynomials, the first quotient term is the ratio of the highest-degree terms in the numerator and denominator: x^3/x^2 = x.

This fact eliminates all but choices A and C.

The denominator of the remainder term is the denominator of the original expression, so will be x^2 +2x +1, as shown in choice A.

So, simply based on a couple of facts about long division (that you learned in the early elementary grades), you can make the correct choice of answer without actually working the problem in detail.

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This is a polynomial long division problem. It is worked in virtually the same way that numerical long division problems are worked: first you find a quotient term, then you multiply that by the divisor and subtract the result from the dividend. The difference is the new dividend. These steps are identical to numerical long division.

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As mentioned above, the quotient term is computed only from the highest-degree terms of dividend and divisor, so that part is actually simpler than for numerical long division.

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Numerical example: 18/7 = 2 remainder 4 or 2 4/7.

8 0

3 years ago

Find the value of the variable.

nalin [4]

Answer:

The variable, y is 11°

Step-by-step explanation:

The given parameters are;

in triangle ΔABC; ${}$ in triangle ΔFGH;

Segment $\overline {AB}$ = 14 ${}$ Segment $\overline {FG}$ = 14

Segment $\overline {BC}$ = 27 ${}$ Segment $\overline {GH}$ = 19

Segment $\overline {AC}$ = 19 ${}$ Segment $\overline {FH}$ = 2·y + 5

∡A = 32° ${}$ ∡G = 32°

∡A = ∠BAC which is the angle formed by segments $\overline {AB}$ = 14 and $\overline {AC}$ = 19

Therefore, segment $\overline {BC}$ = 27, is the segment opposite to ∡A = 32°

Similarly, ∡G = ∠FGH which is the angle formed by segments $\overline {FG}$ = 14 and $\overline {GH}$ = 19

Therefore, segment $\overline {FH}$ = 2·y + 5, is the segment opposite to ∡A = 32° and triangle ΔABC ≅ ΔFGH by Side-Angle-Side congruency rule which gives;

$\overline {FH}$ ≅ $\overline {BC}$ by Congruent Parts of Congruent Triangles are Congruent (CPCTC)

∴ $\overline {FH}$ = $\overline {BC}$ = 27° y definition of congruency

$\overline {FH}$ = 2·y + 5 = 27° by transitive property

∴ 2·y + 5 = 27°

2·y = 27° - 5° = 22°

y = 22°/2 = 11°

The variable, y = 11°

8 0

2 years ago

Help me with this one

Artist 52 [7]

9514 1404 393

Answer:

"complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

(x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

2a = 1

a = 1/2

That means we can write ...

(x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

$x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}$

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Another way to consider this is ...

x² +bx +c

= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

= (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

x² +x +1 = (x +1/2)² +(1 -(1/2)²)

= (x +1/2)² +3/4

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* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

5 0

2 years ago

a school paid $31.50 for each calculator, if the school spent 504 dollars on calculators how many did the school buy?

monitta

The school bought 16 calculators.

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2 years ago

-5y - 6bStep 1 of 2: Identify the first term of the algebraic expression. Indicate whether theterm is a variable term or a const

ira [324]

Answer:

a. Variable term

b. Variable term

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a) We were given the algebraic expression:

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The variable is "y" and its coefficient is "-5"

b) We were given the algebraic expression:

$-5y-6b$

The second term of the algebraic expression is:

$-6b$

The second term is a variable term

The variable is "b" and the coefficient is "-6"

6 0

1 year ago

One of the interior angles of a regular polygon is 144. fine the number of sides of the polygon ​

One of the interior angles of a regular polygon is 144. fine the number of sides of the polygon