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
well if that's in a math problem then its division. Because you are sharing equally.
Answer:
x = 
Step-by-step explanation:
7.4x + 4.1(2x − 4) = −2.3(x − 6) − 21.6
Multiply both sides by 10:
7.4x×10+4.1(2x-4)×10=-2.3(x-6)×10-21.6×10
Refine:
74x+41(2x-4)=-23(x-6)-216
Distributive Property:
74x+82x-164=-23(x-6)-216
Combine like terms:
156x-164=-23(x-6)-216
Distributive Property:
156x-164=-23x+138-216
Combine like terms:
156x-164=-23x-78
Add 164 to both sides:
156x-164+164=-23x-78+164
Simplify:
156x=-23x+86
Add 23x to both sides:
156x+23x=-23x+86+23x
Simplify:
179x=86
Divide both sides by 179:
=
Simplify:
x =
Answer:
32
Step-by-step explanation:
plug in
1/2 (3(3)+4(25)+5) - ((5)2+5(3))
inside parentheses first
1/2 (114) - (25)
multiply
57 - 25
subtract
32
