All categories

3 years ago

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

Mathematics

1 answer:

horsena [70]3 years ago

6 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°.

You might be interested in

What is 5 multiplied by 2

OleMash [197]

10.

5 multiplied by 2 "5 x 2" = 10

6 0

3 years ago

Nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. If the assi

meriva

Answer:

The probability is 0.8

Step-by-step explanation:

The key to answering this question is considering the fact that the two married employees be treated as a single unit.

Now what this means is that we would be having 8 desks to assign.

Mathematically, the number of ways to assign 8 desks to 8 employees is equal to 8!

Now, the number of ways the couple can interchange their desks is just 2 ways

Thus, the number of ways to assign desks such that the couple has adjacent desks is 2(8!)

The number of ways to assign desks among all six employees randomly is 9!

Thus, the probability that the couple will have adjacent desks would be ;

2(8!)/9! = 2/9

This means that the probability that the couple have non adjacent desks is 1-2/9 = 7/9 = 0.77778

Which is 0.8 to the nearest tenth of a percent

4 0

3 years ago

Solve for x 5x2-4x=6

azamat

Answer:

Step-by-step explanation:

5x2 is 10 subtract that and add it to 6 which gives you -4 then you do -4/-4 which is 1

6 0

3 years ago

The number A of tablet computers sold (in millions) can be modeled by the function A=4.5t2+43.5t+17 , where t represents the num

Rina8888 [55]

The problem indicates that A represents the number of tablet computers sold in millions. So, if 65 million were sold, we must substitute A = 65 to the equation. Then, we find for t.

65 = 4.5t² +43.5t + 17
Solving for t using a calculator,
t = 1 and -10.67

Let's take the positive root. So, t=1.
That means the year would be 1 year after 2010. <em>Therefore, the answer is 2011.</em>

6 0

2 years ago

(WILL GIVE BRAINLYIST IF ANSWER IS RIGHT!)

d1i1m1o1n [39]

Answer:

The answer is 1 and 4

Step-by-step explanation:

.25 x 4y = Y

36 divided by 4 = 9

6 0

3 years ago