Lynn L.

asked • 03/24/15# I need to find the value of x in a rhombus.

I need to find the value of x in a rhombus. The equations I'm given are for half of a corner angle on the top right corner and half of a corner angle on the top left corner.

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## 2 Answers By Expert Tutors

Nathan B. answered • 03/24/15

Tutor

5
(20)
Elementary and Algebraic skilled

The angles you gave me aren't opposing, correct. I did not say that they were. I was meaning in ∠ABCD, A and C are opposite and equal, as are B and D.

Now that I have the equations, I can help you further.

What you need is to move the 420 back to the other side. That way, you have a quadratic formula:

16x

^{2}+ 4x - 420 = 0We can factor out a 4 from the equation and then divide both sides by 4:

4(4x

^{2}+ x - 105) = 04x

^{2}+ x - 105 = 0That 4 in front gives us several possibilities to waste time with factoring, so let's try the quadratic formula:

x = (-b ± √(b

^{2}- 4ac)) / 2ax = (-1 ± √1

^{2}- 4 * 4 * -105)) / 2 * 4x = (-1 ± √1

^{2}+ 1680)) / 8x = (-1 ± √1681)) / 8

x = (-1 ± 41) / 8

x = (-1 + 41) / 8 Since we can't have a negative degree

x = 40/8

x = 5

16x^2+4x=420

16x^2+4x-420=0

divide both sides by 4

4x^2+x-105=0

factor

4*105=2*2*3*5*7=(2*2*5)*(3*7)=20*21 and 21-20=1, the coefficient of x

(4x )(x )=0 so far

(4x 21)(x 5)=0 so far

(4x+21)(x-5)=0

x-5=0 or 4x+21=0 but x can't be negative because we are talking about interior angles of a rhombus

x-5=0

x=5

your angles, according to your expressions, are 60º and 30º (these are half-angles)

the 4 angles are 120, 120, 60, and 60

Arthur D.

tutor

you have a quadratic equation and you must factor it and solve for x

I factored 4x^2+x-105=0 and got x=5

substitute x=5 into your expressions to get the half-angles; multiply by 2 to get the whole angle

3x^2-15=3*5^2-15=3*25-15=75-15=60 and 2*60=120º

x^2+x=5^2+5=25+5=30 and 2*30=60º

two angles each equal 120 degrees and two angles each equal 60 degrees

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03/24/15

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Nathan B.

03/24/15