Quadrilaterals

In the diagram above, ABCD is a rhombus. \( \angle{CAD} = 52^\circ \). Find \( \angle{ABD} \).

Diagonals bisect the angles they pass through.

\[ \begin{align} \angle{CAB} &= 2\ \angle{CAD}\ (\mathrm{diagonals\ bisect\ the\ angles}) \\ &= 104^\circ \end{align}\ \]

\( \angle{CAB} \) is co-interior to \( \angle{ABD} \).

\[ \begin{align} \angle{CAB} + \angle{ABD} &= 180^\circ \ (\mathrm{co-interior\ angles,\ }CA \parallel DB) \\ \angle{ABD} &= 180^\circ - 104^\circ \\ &= 76^\circ \end{align}\ \]

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Look through the options below and select the one you think is the best response. You will gain most benefit if you work the problem with pen and paper as you go, i.e. decide what you think is the correct option and write down what you think the result will be before you click. If the next step doesn't display, click another option.

Can you use a property of a rhombus to find the value of other angles in the diagram?

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