Question

in the rectangle below, ( bd = 8x - 2 ), ( ae = 23 ), and ( mangle edc = 41^{circ} ).
find the value of ( x ) and ( mangle ead ).

Explanation:

Step1: Use the property of rectangle's diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(BD = 2AE\).
Given \(BD=8x - 2\) and \(AE = 23\), then \(8x-2=2\times23\).

Step2: Solve the equation for \(x\)

$$
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$$

Step3: Find \(m\angle EAD\)

Since \(ABCD\) is a rectangle, \(AB\parallel CD\), so \(\angle BAC=\angle EDC = 41^{\circ}\) (alternate - interior angles).
Also, \(AE = DE\) (diagonals of a rectangle bisect each other), so \(\triangle ADE\) is isosceles.
\(m\angle EAD=90^{\circ}-41^{\circ}=49^{\circ}\)

Answer:

\(x = 6\), \(m\angle EAD=49^{\circ}\)