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
Answer:
46080 ft²
Step-by-step explanation:
Given :
Scale :
1 in = 4 feets
Recall :
I foot =. 12 inches
Length of drawing = 4 feets
Length of drawing in inches = 4 * 12 = 48 inches
Width of drawing = 5 feets
Width of drawing in inches = 5 * 12 = 60 inches
Actual length of pool = 48 * 4 = 192 feets
Actual width of pool = 60 * 4 = 240 feets
The actual area of the pool :
Length * width
192 feets * 240 feets = 46080 ft²
Answer: Two planes meet in exactly one point
Two lines meet at exactly two points
Step-by-step explanation:
From the given statements there are two statements which are never true :-
1) Two planes meet in exactly one point .
Since when two line meets , they either meet at one point or infinite points (coincidence) , thus its impossible that they will meet at exactly two points.
2) Two lines meet at exactly two points
Since when two planes meet , the intersection of two plane always make a line not a point. Thus its impossible.
