Question

The figure shown is a rhombus. If the measure of angle DAB = 115 degrees, what is the measure of angle ADE?

Answers

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 \( \boxed{115^\circ} \).