Basic Mathematics
# Angles and Lines

$AB$ 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 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).