SOLUTION: The diagonals of rhombus ABCD intersect at E. If m∠BAE = 2/3 (m∠ABE), find m∠BCD.

Algebra ->  Parallelograms -> SOLUTION: The diagonals of rhombus ABCD intersect at E. If m∠BAE = 2/3 (m∠ABE), find m∠BCD.       Log On


   

Question 1188326: The diagonals of rhombus ABCD intersect at E. If m∠BAE = 2/3 (m∠ABE), find m∠BCD.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!


The diagonals of a rhombus are perpendicular. They also bisect each other, and
also bisect the interior angles of the rhombus.

So triangle ABE is a right triangle, so ∠BAE and ∠ABE are complementary, and
so m∠BAE + m∠ABE = 90o. Since m∠BAE = 2/3(m∠ABE), we substitute:

m∠BAE + m∠ABE = 90o
2/3 m∠ABE + m∠ABE = 90o
2/3 m∠ABE + 3/3 m∠ABE = 90o
5/3 m∠ABE = 90o
5 m∠ABE = 270o
m∠ABE = 54o

Substitute in

m∠BAE + m∠ABE = 90o
m∠BAE + 54o = 90o
m∠BAE = 36o

Since diagonals of a rhombus bisect the interior angles,

m∠BAD = 2(36o)
m∠BAD = 72o

Since opposite angles in a rhombus are equal in magnitude,

m∠BCD = 72o

Edwin