AB = BC, so 3x-2 = 2x+4. Also, BC = CA, so 2x+4=x+10.
Solve this system of linear equations:
3x-2 = 2x+4
2x+4=x+10 => x=6
Check: Does AB=BC? Does AB=BC?
Does 3(6)-2 = 2(6)+4? Does 16=16? YES.
Does BC = CA? Does 2(6)+4 = 6+10? YES
x = 6 (answer)
The interior and exterior triangles are related because they are in the pyramid x + c = Triangle so thats how
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A=Lw
P=2L+2w
216=Lw
W=216/L...substitute to Perimeter equation
60=2L+2(216/L)
60L=2L^2 + 432
2L^2-60L+432=0
2(L^2 - 30L + 216)=0
2(L-18)(L-12)=0
L=12, W=18 or L=18, W=12
Answer:
- complement: 32.8°
- supplement: 122.8°
Step-by-step explanation:
The sum of an angle A and its complement C is 90°:
A + C = 90°
C = 90° -A . . . . . subtract A from both sides.
That is, the complement of an angle is found by subtracting the angle from 90°.
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The sum of an angle and its supplement is 180°. This means the supplement of an angle is found by subtracting the angle from 180°. You may notice the supplement is 90° more than the complement.
A + S = 180°
S = 180° -A = 90° +(90° -A)
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For the given angle, the complement is ...
C = 90° -57.2° = 32.8°
And the supplement is ...
S = 180° -57.2° = 122.8°
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<em>Additional comment</em>
We generally like angle measures to be positive (as with all measures in geometry). Hence, we might say that the complement of an angle greater than 90° does not exist. YMMV
