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Allushta [10]
3 years ago
15

The measure of one angle of an octagon is two times smaller that of the other seven angles. What is the measure of each angle?

Mathematics
1 answer:
Anestetic [448]3 years ago
7 0

Answer:

7 of the angles measure 144 degrees each and one angle measures 72 degrees

Step-by-step explanation:

Let

x -----> represent the measures of the seven same-size angles,

x/2 ----> represent the measure of the one that is "two times smaller."

we know that

The sum of internal angles of a polygon can be calculated as:

S=180^o(n-2)

where

n is the number of sides of the polygon

In this case

n=8 (octagon)

substitute

S=180^o(8-2)=1,080^o

so

The linear equation that represent this problem is

\frac{x}{2}+7x=1,080

solve for x

\frac{15x}{2}=1,080\\\\15x=2,160\\\\x=144^o

so

\frac{x}{2}=72^o

therefore

7 of the angles measure 144 degrees each and one angle measures 72 degrees

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Find the equation of the circle with center at (-1, 3) and radius of 4.
Nataly [62]

Answer:

(x+1)^2 + (y-3)^2 = 16

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2

Where (h,k) is the center and r is the radius

(x--1)^2 + (y-3)^2 = 4^2

(x+1)^2 + (y-3)^2 = 4^2

(x+1)^2 + (y-3)^2 = 16

7 0
3 years ago
A rectangle has a length four more than
torisob [31]
L ≥ 5w + 4
2(L+w) ≥ 32

L+w ≥ 16

6w + 4 ≥ 16
6w ≥ 12
w ≥ 2

L ≥ 5w + 4
L ≥ 14

If L = 14 and w = 2 then the perimeter is 32.
These are the smallest dimensions that fit the criteria.

Note: If we raise the width by 1 to w = 3
then the length is at least 19. At 19 by 3 we have P = 44
Like would be appreciated!!
8 0
1 year ago
Hi! This is a fairly simple question for some of you, but I wanted to ask, how do you solve this? Thank you so much! :)
givi [52]
Hey I got to it c c c c c c c c c c c c c c c c 8 8
5 0
3 years ago
36 is 72% of what number
Dmitry_Shevchenko [17]
36/72=0.5
0.5*100=50
Therefore 36 is 72% of 50

Hope this helps :)
5 0
3 years ago
Read 2 more answers
What is the polynomial of 3,4
Sav [38]

The degree of a polynomial is the highest power of x in its expression. Constant (non-zero) polynomials, linear polynomials, quadratics, cubics and quartics are polynomials of degree 0, 1, 2 , 3 and 4 respectively. The function f(x)=0 is also a polynomial, but we say that its degree is 'undefined'.



7 0
3 years ago
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