Answers
Check the picture below.
there are a few angles shaded, I'll call that angle at O ∡O, and that angle at "x" ∡x and the green angle at A, ∡A, and the angle at B, ∡B, just so you know which angle we're referring to.
well, first off let's notice that B and C are points of tangency, meaning we get right-angles as you see in the picture, if we run an angle bisector from ∡x, towards point O, we get two congruent triangles, lemme shorten that up some, 90 + 90 + ∡O +∡x = 360, which means that ∡O + ∡x = 180, meaning that ∡O = 180 - ∡x, if that's so, the angle at point O across the shade, is 360 - ∡O or 360 - (180 - ∡x).
alrighty, by the inscribed angle theorem, ∡A is half of ∡O.
let's now focus on the triangle AOB, we'll be using half of ∡A and half of ∡O and ∡B on that triangle, let's proceed.
[tex]\measuredangle x + \measuredangle O=180\implies \measuredangle O=180-\measuredangle x \\\\\\ \measuredangle A = \cfrac{\measuredangle O}{2}\implies \measuredangle A = \cfrac{180-\measuredangle x}{2} \\\\\\ \stackrel{\textit{the angle across from }\measuredangle O~is}{360-\measuredangle O}\implies 360-(180 - \measuredangle x)\implies 180+\measuredangle x \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\large the sum of all three angles at }\triangle AOB}{\stackrel{\textit{half of }\measuredangle A}{\cfrac{1}{2}\cdot \cfrac{180-\measuredangle x}{2}}~~ + ~~\stackrel{\textit{half the angle across from }\measuredangle O}{\cfrac{180+\measuredangle x}{2}}~~ +~~\measuredangle B~~ =~~180} \\\\\\ \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B = 180[/tex]
now, let's multiply both sides by the LCD of all denominators, hmmmm in this case that'll be 4, so multiplying both sides by the LCD will do away with the denominators, so let's do so.
[tex]4\left( \cfrac{180-\measuredangle x}{4}+\cfrac{180+\measuredangle x}{2}+\measuredangle B \right) = 4(180) \\\\\\ (180-\measuredangle x)+2(180+\measuredangle x)+4\measuredangle B = 720 \\\\\\ (180-\measuredangle x)+(360+2\measuredangle x)+4\measuredangle B = 720\implies 540+\measuredangle x+4\measuredangle B = 720[/tex]
[tex]\measuredangle x+4\measuredangle B = 180\implies 4\measuredangle B = 180-\measuredangle x\implies \measuredangle B = \cfrac{180-\measuredangle x}{4} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \measuredangle B = 45 - \cfrac{\measuredangle x}{4}~\hfill[/tex]
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Answer:
9
Step-by-step explanation:
12/4=3
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Filler and more filler
The area of the square is 9 [tex]cm^{2}[/tex].
What is area?The space occupied by a flat shape or the surface of an object is called area.
Formula for the area of square?[tex]Area = a^{2}[/tex]
Where, a is the length of the side of a square
What is perimeter?Perimeter is the total length of the sides of a two-dimensional shape.
Formula for the perimeter of squarePerimeter of a square = 4a
Where, a is the side of a square
According to the given question
Perimeter of a square is 12cm.
Let a be the length of the side of a square.
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Perimeter of the square = 4a
⇒ 12 = 4a
⇒ a = 12/4
⇒ a = 3cm
So, the area of square = 3cm × 3cm = 9 square cm
Hence, the area of the square is 9 [tex]cm^{2}[/tex].
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Answer:
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x = -2
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Answer:
Step-by-step explanation:
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Answer:
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Answer:
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Answer:
50 miles
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Step-by-step explanation:
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Answer:
It's attached
Step-by-step explanation:
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(Attached)
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Answers
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Step-by-step explanation:
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Answers
a.
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Answer:
wat?
Step-by-step explanation:
merry christmas....yey!!
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Step-by-step explanation:
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Admission to the state fair is $12, and each ride ticket costs $3.50. Write an
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Answer:
Step-by-step explanation:
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Answer:
4900
Step-by-step explanation:
70^2 means 70*70
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Answer:
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Answers
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Answer:
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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