Question
The figure shown is a rhombus. If the measure of angle DAB = 115 degrees, what is the measure of angle ADE?
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Answered by
GPT-4o mini
In a rhombus, opposite angles are equal, and adjacent angles are supplementary. This means that if we know one angle, we can determine the others.
Given that \( \angle DAB = 115^\circ \), we can find the adjacent angle \( \angle ABC \):
\[
\angle ABC = 180^\circ - \angle DAB = 180^\circ - 115^\circ = 65^\circ
\]
Since opposite angles in a rhombus are equal, we have:
\[
\angle DCB = \angle DAB = 115^\circ
\]
And since \( \angle ABC \) is also adjacent to \( \angle ADE \), we can use the supplementary property again:
\[
\angle ADE = 180^\circ - \angle ABC = 180^\circ - 65^\circ = 115^\circ
\]
Thus, the measure of angle \( \angle ADE \) is also:
\[
\angle ADE = 115^\circ
\]
Thus, the measure of angle \( ADE \) is \( \boxed{115^\circ} \).
Given that \( \angle DAB = 115^\circ \), we can find the adjacent angle \( \angle ABC \):
\[
\angle ABC = 180^\circ - \angle DAB = 180^\circ - 115^\circ = 65^\circ
\]
Since opposite angles in a rhombus are equal, we have:
\[
\angle DCB = \angle DAB = 115^\circ
\]
And since \( \angle ABC \) is also adjacent to \( \angle ADE \), we can use the supplementary property again:
\[
\angle ADE = 180^\circ - \angle ABC = 180^\circ - 65^\circ = 115^\circ
\]
Thus, the measure of angle \( \angle ADE \) is also:
\[
\angle ADE = 115^\circ
\]
Thus, the measure of angle \( ADE \) is \( \boxed{115^\circ} \).
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