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Angles and Lines

Angles and Lines: Level 3 Challenges


ABAB is parallel to CDCD and AB=2CDAB =2CD.

If mABC=45om\angle ABC = 45^o and mCBD=15o,m\angle CBD = 15^o, find mBADm\angle BAD in degrees.

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

In a quadrilateral ABCDABCD, ABD=BCA=CDB=DAC=30\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.

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

Lines ll and mm are parallel. MM, NN and OO are points such that MM is on ll and NN is on mm and OO is between the two lines. If the smaller angle between ll and MOMO is 3535^{\circ} and MON=105\angle MON = 105^{\circ}, find the acute angle between mm and NONO.

Clarification: The diagram is not accurate

Find xx (in degrees).


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