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Homework Help: Geometry

Posted by Allison on Sunday, December 11, 2011 at 7:42pm.

If m<DBC=10x and m<ACb=4x^2, find m<ACB.
The quadrilateral ABCD is a rectangle.
B ------------- C
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| |
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A -------------|D
There are diagonal bisectors inside the rectangle but I could not draw them in. The diagonals are DB and CA and the point in the middle is E.

• Geometry - Steve, Monday, December 12, 2011 at 6:19pm

  Let E be where the diagonals intersect.
  Since ABCD is a rectangle, the diagonals are the same length, and bisect each other.
  
  Thus, EB = EC and the triangle BCE is isosceles, making m<DBC = m<ACB
  
  So,
  10x = 4x^2
  10 = 4x
  x = 5/2 = 2.5
  
  <DBC = 25°
  <ACB = 25°
  

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