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3 years ago

Congruent angle pairs : Find value of x

Mathematics

1 answer:

Alexandra [31]3 years ago

6 0

Answer:

(Opt.B) 18

Step-by-step explanation:

4x = 2y - x (vertically opposite angles are equal)

4x + x = 2y

5x = 2y ----- (1)

4x + 2y + x = 180 (Linear pair angles)

5x + 2y = 180

From (1) we can understand that, the value of 5x and 2y is the same. So,

5x + 5x = 180

10x = 180

x = 180/10

x = 18

Just completing,

Putting the value of x in (1)

5*18 = 2y

90 = 2y

90/2 = y

45 = y

Hope you understand

Please mark as brainliest

Thank You

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2 years ago

If y varies jointly with x and z, and y = 200 when x = 8 and z = 10, what is x when y = 165 and z = 11?

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The answer is 2.5

The next blank is 6

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3 years ago

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How to prove this???

swat32

$\cos^3 2A + 3 \cos 2A \\
\Rightarrow \cos 2A (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (\cos^2 2A + 3) \\
\Rightarrow (\cos^2 A - \sin^2 A) (1 - \sin^2 2A + 3) \\
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\Rightarrow (\cos^2 A - \sin^2 A) (4 - (2\sin A \cos A)(2\sin A \cos A)) \\
\Rightarrow (\cos^2 A - \sin^2 A) (4 - 4\sin^2 A \cos^2 A) \\ 
\Rightarrow 4(\cos^2 A - \sin^2 A) (1 - \sin^2 A \cos^2 A) 
$

go to right side now

$4( \cos^6 A - \sin^6 A)\\
\Rightarrow 4( \cos^3 A - \sin^3 A)(\cos^3 A + \sin^3 A)$

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\Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\
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so $\sin^2 A + \cos^2 A = 1$

$4( \cos^6 A - \sin^6 A)\\ \Rightarrow 4(\cos A - \sin A)(\cos^2 A + \cos A \sin A + \sin^2 A) \\ ~\quad \quad\cdot ( \cos A + \sin A)(\cos^2 A - \cos A \sin A + \cos^2 A) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 + \cos A \sin A )(1- \cos A \sin A ) \\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \cos^2 A \sin^2 A )\\ \Rightarrow 4(\cos^2 A - \sin^2 A)(1 - \sin^2 A \cos^2 A ) \\
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Y $\alpha$ x
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