ABCD is a rhombus. Find 'x'?

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1 Answer
Jim G.
Nov 19, 2017

#x=54^@#

Explanation:

#"using the properties of the rhombus"#

#• " the diagonals bisect the angles"#

#• " the diagonals bisect each other at right angles"#

#• " opposite sides are parallel"#

#" BD is a diagonal and bisects "angleADC#

#rArrangleADB=angleCDB=x#

#angleABD=angleCDB=x rarrcolor(blue)"alternate angles"#

#"the sum of the angles in the lower triangle" =180^@#

#rArr36^@+90^@+x=180#

#rArrx=180-36-90=54^@#

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