Geometry

Angles and Lines

Angles and Lines: Level 3 Challenges

         

\(AB\) is parallel to \(CD\) and \(AB =2CD\).

If \(m\angle ABC = 45^o \) and \(m\angle CBD = 15^o,\) find \(m\angle BAD\) in degrees.

In the square above, \(E\) and \(F\) are the midpoints of \(\overline{BC}\) and \(\overline{CD} ,\) respectively. If \(G\) is the intersection point of \(\overline{AC}\) and \(\overline{BF}\) and \(x=\angle AEG,\) find \(x\) (in degrees) in terms of \(\alpha.\)

In a quadrilateral \(ABCD\), \(\angle ABD = \angle BCA = \angle CDB = \angle DAC = 30^\circ\).

Find the smaller of the two angles (in degrees) between the diagonals AC and BD.

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Note: The image might not be necessarily up to scale.

Lines \(l\) and \(m\) are parallel. \(M\), \(N\) and \(O\) are points such that \(M\) is on \(l\) and \(N\) is on \(m\) and \(O\) is between the two lines. If the smaller angle between \(l\) and \(MO\) is \(35^{\circ}\) and \(\angle MON = 105^{\circ}\), find the acute angle between \(m\) and \(NO\).


Clarification: The diagram is not accurate

Find \(x\) (in degrees).

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