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2 years ago

In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?

Mathematics

1 answer:

coldgirl [10]2 years ago

6 0

Given that

In a Parallelogram CARS ,∠C = (5x-20)°

∠A = (3x+20)°

angle C and angle A are adjacent angles

We know that

In a Parallelogram the adjacent angles are supplementary.

⇛∠C + ∠A = 180°

⇛ (5x-20)°+(3x+20)° = 180°

⇛5x°-20°+3x°+20° = 180°

⇛(5x°+3x°)+(20°-20°) = 180°

⇛8x°+0 = 180°

⇛8x° = 180°

⇛ x° = 180°/8

⇛ x° = 22.5°

Answer:-The value of x = 22.5°

also read similar questions: In parallelogram MATH, m= (3x+ 20) and t= (5x-4) find A

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find the value of x (5x+12) (3x+8) a 10 b 15 c 20 d 25

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Find the solution of the following equation whose argument is strictly between 270^\circ270 ∘ 270, degree and 360^\circ360 ∘ 360

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$\rightarrow z^4=-625\\\\\rightarrow z=(-625+0i)^{\frac{1}{4}}\\\\\rightarrow x+iy=(-625+0i)^{\frac{1}{4}}\\\\ x=r \cos A\\\\y=r \sin A\\\\r \cos A=-625\\\\ r \sin A=0\\\\x^2+y^2=625^{2}\\\\r^2=625^{2}\\\\|r|=625\\\\ \tan A=\frac{0}{-625}\\\\ \tan A=0\\\\ A=\pi\\\\\rightarrow z= [625(\cos (2k \pi+pi) +i \sin (2k\pi+ \pi)]^{\frac{1}{4}}\\\\k=0,1,2,3,4,....\\\\\rightarrow z=(625)^{\frac{1}{4}}[\cos \frac{(2k \pi+pi)}{4} +i \sin \frac{(2k\pi+ \pi)}{4}]$

$\rightarrow z_{0}=(625)^{\frac{1}{4}}[\cos \frac{pi}{4} +i \sin \frac{\pi)}{4}]\\\\\rightarrow z_{1}=(625)^{\frac{1}{4}}[\cos \frac{3\pi}{4} +i \sin \frac{3\pi}{4}]\\\\ \rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]\\\\ \rightarrow z_{3}=(625)^{\frac{1}{4}}[\cos \frac{7\pi}{4} +i \sin \frac{7\pi}{4}]$

Argument of Complex number

Z=x+iy , is given by

If, x>0, y>0, Angle lies in first Quadrant.

If, x<0, y>0, Angle lies in Second Quadrant.

If, x<0, y<0, Angle lies in third Quadrant.

If, x>0, y<0, Angle lies in fourth Quadrant.

We have to find those roots among four roots whose argument is between 270° and 360°.So, that root is

$\rightarrow z_{2}=(625)^{\frac{1}{4}}[\cos \frac{5\pi}{4} +i \sin \frac{5\pi}{4}]$

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3 years ago

In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?​

In a Parallelogram CARS , <C = 5x-20 and <A = 3x+20. Find the value of x ?