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Question
In the diagram above, quadrilateral ABCD is a rhombus. If the m ∠DAB
= 124 °
find the measurements below.
Answers
GPT-4o mini
In a rhombus, opposite angles are equal, and adjacent angles are supplementary. Given that the measure of angle \( \angle DAB = 124^\circ \), we can find the other angles of the rhombus:
1. **Find \( \angle ABC \):**
Since adjacent angles in a rhombus are supplementary, we have:
\[
\angle ABC = 180^\circ - \angle DAB = 180^\circ - 124^\circ = 56^\circ.
\]
2. **Find \( \angle BCD \):**
Opposite angles are equal in a rhombus, so:
\[
\angle BCD = \angle DAB = 124^\circ.
\]
3. **Find \( \angle CDA \):**
Again, since \( \angle CDA \) is opposite to \( \angle ABC \):
\[
\angle CDA = \angle ABC = 56^\circ.
\]
In summary, the angle measures in rhombus ABCD are:
- \( \angle DAB = 124^\circ \)
- \( \angle ABC = 56^\circ \)
- \( \angle BCD = 124^\circ \)
- \( \angle CDA = 56^\circ \)
If you have any other specific measurements or angles to calculate, please let me know!
1. **Find \( \angle ABC \):**
Since adjacent angles in a rhombus are supplementary, we have:
\[
\angle ABC = 180^\circ - \angle DAB = 180^\circ - 124^\circ = 56^\circ.
\]
2. **Find \( \angle BCD \):**
Opposite angles are equal in a rhombus, so:
\[
\angle BCD = \angle DAB = 124^\circ.
\]
3. **Find \( \angle CDA \):**
Again, since \( \angle CDA \) is opposite to \( \angle ABC \):
\[
\angle CDA = \angle ABC = 56^\circ.
\]
In summary, the angle measures in rhombus ABCD are:
- \( \angle DAB = 124^\circ \)
- \( \angle ABC = 56^\circ \)
- \( \angle BCD = 124^\circ \)
- \( \angle CDA = 56^\circ \)
If you have any other specific measurements or angles to calculate, please let me know!