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Properties of Rectangles


The above diagram shows a rectangle creased at \(EF\) such that that point \(C\) aligns with point \(A.\) If \(\angle BAE=38^\circ,\) what is \(\angle EFD\) in degrees?

Note: The above figure is not drawn to scale.

The figure above depicts a rectangle with \(\overline{AB}=5\) and \(\overline{AD}=13.\) Find \(x+y.\)

\(ABCD\) is a square. On line segment \(AB\), \(E\) is a point such that \(\angle ADE = 37 ^\circ\). What is the measure of \(\angle EDC\) (in degrees)?

In the diagram above, \(\square BCDE\) is a rectangle with horizontal side length \(30\) cm and vertical side length \(6\) cm. Line segments \(\overline{BD}\) and \(\overline{CE}\) are diagonals of \(\square BCDE,\) which intersect at point \(O\). Point \(M\) is the bisector of \(\overline{BE},\) and the extension of lines \(\overline{DM}\) and \(\overline{CB}\) intersect at point \(A.\) If point \(F\) is the intersection of \(\overline{CE}\) and \(\overline{AD},\) what is the area of \(\triangle DOF?\)

Note: The above figure is not drawn to scale.

The diagram above shows a circle centered at \(O,\) with rectangle \( ODCE\) inscribed in the quarter circle \(AOB.\) If the radius of the circle is \(14\), what is the length of line segment \(\overline{DE}?\)


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