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.
 
 

Nathan B.

tutor
The opposing angles of a rhombus are congruent (the same amount).
The total of all the angles equal 360.
If you have half of an angle, you can multiply each half angle by 2 to get the full angle. Once you have the full angle, 2*one of the given angles + 2*the other angle given should = 360
 
You don't mention what x is in your problem that you're trying to solve.
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03/24/15

Lynn L.

These angles aren't opposing.  One is at the left hand corner, the other is at the right corner, so they would not necessarily be equal.  This is what I've got so far:
 
4(3x^2-15) + 4(x^2+x) = 360 degrees
12x^2 - 60 + 4x^2 + 4x = 360
16x^2 + 4x = 420
I can't figure out where to go from here.
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03/24/15

Lynn L.

So I take it you can't help me any further?
 
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03/24/15

2 Answers By Expert Tutors

By:

Nathan B. answered • 03/24/15

Elementary and Algebraic skilled

Nathan B.

tutor
Sorry for the slow response. I was helping another student's question as I was waiting for you to inform me more.
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03/24/15

Lynn L.

Oh no problem.  Thanks for the help!
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03/24/15

Arthur D. answered • 03/24/15

Effective Mathematics Tutor

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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