Problem 1
x = measure of angle N
2x = measure of angle M, twice as large as N
3(2x) = 6x = measure of angle O, three times as large as M
The three angles add to 180 which is true of any triangle.
M+N+O = 180
x+2x+6x = 180
9x = 180
x = 180/9
x = 20 is the measure of angle N
Use this x value to find that 2x = 2*20 = 40 and 6x = 6*20 = 120 to represent the measures of angles M and O in that order.
<h3>Answers:</h3>
- Angle M = 40 degrees
- Angle N = 20 degrees
- Angle O = 120 degrees
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Problem 2
n = number of sides
S = sum of the interior angles of a polygon with n sides
S = 180(n-2)
2700 = 180(n-2)
n-2 = 2700/180
n-2 = 15
n = 15+2
n = 17
<h3>Answer: 17 sides</h3>
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Problem 3
x = smaller acute angle
3x = larger acute angle, three times as large
For any right triangle, the two acute angles always add to 90.
x+3x = 90
4x = 90
x = 90/4
x = 22.5
This leads to 3x = 3*22.5 = 67.5
<h3>Answers:</h3>
- Smaller acute angle = 22.5 degrees
- Larger acute angle = 67.5 degrees
<span>With no digit being repeated: 10*9*8*7*6= 30,240</span>
Answer: 
Step-by-step explanation:
Given, A pizza is to be cut into halves.
Since half is represented by 
.
So each piece is now of the original.
if each of these halves is to be cut into sevenths, then the fraction of final pieces would be: 
or we can say each half is divides into 7 pieces since there are two halves, so there will be 2 x 7 = 14 peices.
And the fraction of the pizza is each of the final pieces = .
Answer:
50-(14+12+2(5)+2(2)+3)
50-(26+10+4+3)
50-43
7
Step-by-step explanation:
Hope this Helps
