ABCD is a rhombus. Find 'x'?

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ABCD is a rhombus. Find 'x'?

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Answer 1 · 2017-11-19T13:57:58

$x = 54^{\circ}$ $x=54^@$

Explanation:

$using the properties of the rhombus$ $"using the properties of the rhombus"$

$∙ the diagonals bisect the angles$ $• " the diagonals bisect the angles"$

$∙ the diagonals bisect each other at right angles$ $• " the diagonals bisect each other at right angles"$

$∙ opposite sides are parallel$ $• " opposite sides are parallel"$

$BD is a diagonal and bisects ∠ A D C$ $" BD is a diagonal and bisects "angleADC$

$\Rightarrow ∠ A D B = ∠ C D B = x$ $rArrangleADB=angleCDB=x$

$∠ A B D = ∠ C D B = x \to alternate angles$ $angleABD=angleCDB=x rarrcolor(blue)"alternate angles"$

$the sum of the angles in the lower triangle = 180^{\circ}$ $"the sum of the angles in the lower triangle" =180^@$

$\Rightarrow 36^{\circ} + 90^{\circ} + x = 180$ $rArr36^@+90^@+x=180$

$\Rightarrow x = 180 - 36 - 90 = 54^{\circ}$ $rArrx=180-36-90=54^@$

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ABCD is a rhombus. Find 'x'?

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