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WINSTONCH [101]
3 years ago
13

1. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Sho

w your work.
2. What is the sum of the measures of the exterior angles in a heptagon? Explain.



3. Find the measure of each interior angle and each exterior angles of the following regular polygons. Show your work.
a. Decagon

b. Pentagon

c. Dodecagon

d. 16-gon

e. 25-gon

Mathematics
1 answer:
slavikrds [6]3 years ago
6 0
3. Check the first picture.

let

"a" be the number of angles (or sides)
"t" be the number of triangular regions, that the diagonals drawn from one angle divide the regular polygon into.

it is clear that for a polygon of n-sides, there are n-2 triangular regions, each of which has a total measure of angles equal to 180°.

so the sum of the interior angles of a n-gon is (n-2)180°.

In a regular polygon, the measure of each interior angle is equal, so:

the measure of each interior angle of a regular n-gon is:  \frac{(n-2)180}{n}

apply the formula to each angle.

a. n=10,   \frac{(n-2)180}{n}=\frac{(10-2)180}{10}=(8*180)/10=144
b. n=5,   \frac{(n-2)180}{n}=\frac{(5-2)180}{5}=(3*180)/5=108
c. n=12,   \frac{(n-2)180}{n}=\frac{(12-2)180}{12}=(10*180)/12=150
d. n=16,   \frac{(n-2)180}{n}=\frac{(16-2)180}{16}=(14*180)/16=157.5
e. n=25,   \frac{(n-2)180}{n}=\frac{(25-2)180}{25}=(23*180)/25=165.5

2. 

the sum of the interior angles of a heptagon is (7-2)180°=5*180°=900°

let the measures of the interior angles be a,b,c,d,e,f and g.

so a+b+c+d+e+f+g=900°

the exterior angle measures are 180-a, 180-b, 180-c, 180-d, 180-e, 180-f, 180-g, 

so the sum of the measure angles of the exterior angles is 

(180°-a)+(180°-b) +(180°-c)+(180°-d)+(180°-e)+(180°-f)+(180°-g)
= 180°*7-(a+b+c+d+e+f+g)=1260°-900°=360°.

In fact, the sum of the measures of the exterior angles of any polygon is 360°.

1. Let the length of the second base be x

then 
\frac{x+24}{2}=19
x+24=38
x=38-24=14 units

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how do i get the answer and what is the answer? im looking for a right answer not just someone who types in the mayo mayo
ankoles [38]

Answer:

x = 51°

Step-by-step explanation:

The straight line segment has a total angle of 180°. Therefore, to find the angle inside the triangle that is next to 94°, subtract 94 from 180:

180° - 94° = 86°

That angle is almost a right angle but not quite. Now, to find x, add up the two angles inside the triangle and subtract it from 180°:

43° + 86° = 129°

180° - 129° = 51°

5 0
3 years ago
Lena found a 5/8
DENIUS [597]

Answer:

Naomi had the correct measurement the ring weighed 0.625 carats

Step-by-step explanation:

* The diamond ring weighed 5/8 carats

- To know who is right lets change the fraction 5/8 to a decimal number

∵ 5/8 means 5 ÷ 8

- 5 is smaller than 8 so we will multiply it by 10 and

 insert decimal point in the quotient (answer of division)

∴ It will be 50 ÷ 8 = 6 and remainder 2/8 ⇒ 1/4

∴ The quotient = 0.6 and remainder 1/4

- 1 is smaller than 4 so we will multiply it by 10

∴ It will be 10 ÷ 4 = 2 and remainder 2/4 ⇒ 1/2

∴ The quotient = 0.62 and remainder 1/2

- 1 is smaller than 2 so we will multiply it by 10

∴ It will be 10 ÷ 2 = 5 without remainder

∴ The quotient = 0.625

* Naomi had the correct measurement the ring weighed 0.625 carats

8 0
3 years ago
Read 2 more answers
3t>5t+12 please help me? i suck at math
Alex777 [14]
<span>3t>5t+12
Subtract 5t from both sides to get the variable on only one side.
-2t>12
Divide both sides by -2
Final Answer: t< -6</span>
3 0
3 years ago
Ms.Ellis has a crate that is 5 feet tall, 6 feet wide, and 8 feet long. How many square feet of paint does she need to cover the
Vladimir [108]

Answer:

The answer to your question is 236 ft²

Step-by-step explanation:

Data

height = 5 ft

width = 6 ft

length = 8 ft

Area = ?

Process

I will consider that the crate is a rectangular prism which has 6 sides

1.- Find the area of the sides that measure 8 x 6

Area = 2 (8 x 6)

        = 2(48)

        = 96 ft²

2.- Find the area of the sides that measure 8 x 5

Area = 2(8 x 5)

Area = 2(40)

Area = 80 ft²

3.- Find the area of the sides that measure 6 x 5

Area = 2( 6 x 5)

Area = 2(30)

Area = 60

4.- Find the total area

Area = 96 + 80 + 60

Area = 236 ft²

5.- Conclusion

She needs 236 ft² of paint

3 0
3 years ago
Can you guys pls help me eith this one plsss
Darina [25.2K]
The answer is 16 3/8.

So, to find out the total weight we have to add them all up. However, since we need a common denominator to add them up, we have to change the denominator of the first two mixed fractions, 2 1/2 and 1 1/2. Since we know that 2 is a factor of 8, we know that we can use 8 as the common denominator. The third mixed fraction already has a denominator of 8 so we just have to change the denominator of, 2 1/2 and 1 1/2. To do this, we just have to multiply the numerator and denominator by 4 to get, 2 4/8 and 1 4/8. Next, we can add them all up. We first add the fraction part, 4/8 + 4/8 + 3/8, which would give us 11/8, which can be turned into 1 3/8. Finally, we just have to add the whole numbers and 1 3/8, 2 + 1 + 12 + 1 3/8, to get 16 3/8.

Comment any questions if you still need help.

8 0
1 year ago
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