Answer:
45 or multiples of 45 around the centre of octagon
Step-by-step explanation:
Given that ABCDEFGH is a regular octagon. i.e. it has 8 sides.
Since regular ocagon, all interior angles would be equal.
Sum of all interior angles of octagon = 2(8)-4 right angles
= 12 right angles
Hence each angle = 12(90)/8 = 135 degrees
Thus the octagon when rotated will take the same shape if vertices interchange also due to the property that all sides and angles are equal
Since each angle is 135 imagine an octagon with one vertex at origin O, and adjacent vertex B on x axis. OB has to be coincident with BC the next side or the previous side to get it mapped onto itself
The centre will be at the middle with each side subtending an angle of 45 degrees.
Hence if rotation is done around the centre with 45 degrees we will get octagon mapped onto itself.
45, 90, 135 thus multiples of 45
10 students of Elena's classmates like to make jewellery.
<u>Step-by-step explanation:</u>
Let total no.of classmates who liked the jewellery = x
Here, in the given problem, given she asked her classmates '20'. So, it clearly shows that total number of students/classmates = 20. Also, in that, 50% said like to make jewellery. Now find 'x' as below,



Hence, the total number of classmates who liked to make Jewellery = 10
Answer:
The volume of cone v= 113.04 cm³.
Step-by-step explanation:
Formula used to find volume of cone is:

where r is the radius and h is the height of cone.
In the given question we are given:
height h= 6 cm
diameter d= 6 cm
We know radius r = d/2 = 6/2 = 3 cm
so, volume will be:



So, the volume of cone v= 113.04 cm³ given height h= 6cm and radius r= 3cm
Answer: See the attached image
You have the correct idea for the boxes you've filled out. For the first three boxes in column 1, I would be specific which segments you are dividing. So for instance, in the first box, it would be EG/EB = 55/11 = 5. Then the second box would be EF/EC = 35/7 = 5, and so on. The order of the boxes doesn't matter. The three boxes then combine together to help show that the triangles are similar. Specifically
. The order of the letters is important to help show how the angles pair up and how the sides pair up. We use the SSS similarity theorem here.
The second problem is the same idea, but we use one pair of congruent angles. So we'll use the SAS similarity theorem this time.
2=e^.052t
ln 2=ln e^0.052t=0.052t ln e=0.052t
t=(ln 2)/0.052=13.33 years
☺☺☺☺