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sergeinik [125]
3 years ago
12

the diagram shows a star made by surrounding a regular octagon with triangles, explain why angle a must be 135 degrees

Mathematics
1 answer:
VikaD [51]3 years ago
7 0

Answer:

From the sum of angles on a straight line, given that the rotation of each triangle attached to the sides of the octagon is 45° as they move round the perimeter of the octagon, the angle a which is supplementary to the angle turned by the triangles must be 135 degrees

Step-by-step explanation:

Given that the triangles are eight in number we have;

1)  (To simplify), we consider the five triangles on the left portion of the figure, starting from the bottom-most triangle which is inverted upside down

2) We note that to get to the topmost triangle which is upright , we count four triangles, which is four turns

3) Since the bottom-most triangle is upside down and the topmost triangle, we have made a turn of 180° to go from bottom to top

4) Therefore, the angle of each of the four turns we turned = 180°/4 = 45°

5) When we extend the side of the octagon that bounds the bottom-most triangle to the left to form a straight line, we see the 45° which is the angle formed between the base of the next triangle on the left and the straight line we drew

6) Knowing that the angles on a straight line sum to 180° we get interior angle in between the base of the next triangle on the left referred to above and the base of the bottom-most triangle as 180° - 45° = 135°.

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Question 2 (1 point)
nikdorinn [45]

Answer: 24 hours - no; because depending on where you are on Earth, you have a  different amount of sunlight.

Step-by-step explanation:

The day-night cycle is a complete day or a complete rotation of the earth around its axis. This takes 24 hours which is why 24 hours is the length of a full day.

People around the world however, do not get the same amount of sunlight or darkness and this is because of where they are on Earth. Due to the way the planet is tilted on its axis, some areas see sunlight more than other in a period and others see more darkness.

6 0
3 years ago
A man is filling an empty 5 gallon bucket with water at a constant rate there are 2.4 gallons of water in the bucket after filli
Fiesta28 [93]

2.4g / 12 minutes

0.2g/minutes

Answer is 0.2 gallons per minute

4 0
3 years ago
What is the circumference of the circle? Use a = 3.14. Round your answer to the
larisa [96]

Answer: 53.4 cm

Step-by-step explanation:

The formula for circumference is C=2πr or C=πd. These equations are the same. Since the problem gives us the diameter, we'll go ahead and use C=πd.

C=(3.14)(17)

C=53.38=53.4 cm

3 0
3 years ago
Identify the slope and y-intercept of the graph of the equation. y = 1/4x + 3
Alik [6]
Ooo. 
Fun. 

So the equation: y = 1/4x = 3 is in slope-intercept form where, y = mx + b.
'm' is the slope and 'b' is the y-intercept. 

Knowing this, we can easily conclude that Choice A is the correct answer. 

Why?

Well, just look below.
y=1/4x + 3
y = mx + b

We simply match up the values with the slope-intercept formula and see that 3 falls under the y-intercept category, and m, which always equals slope is replaced by 1/4.

Thus, A is the correct choice.
7 0
3 years ago
HELP!!! Solve the system of equation by graphing : y=x+3 , 2x+y= -6 : also how do you know if it’s substitution or elimination?
schepotkina [342]

Either would work, but substitution looks a bit easier.

The graph for these two is shown below.


I just put the equations in just as they are written. They did not have to be changed in any way. DESMOS is a wonderful program. Very powerful.


The blue line is 2x + y = - 6

The red line is y = x + 3


The best way to solve this other than a graph is to use substitution. Put the red graph into the blue one.

2x + y = - 6

2x +(x + 3) = - 6

2x + x + 3 = - 6

3x + 3 = - 6 Subtract 3 from both sides.

3x = - 6 - 3

3x = - 9

x = -9/3

x = -3


Now go back and solve for y

y = x + 3

y = -3 + 3

y = 0


Answer

The solution point is (-3,0) just what the graph shows.

4 0
3 years ago
Read 2 more answers
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