Question
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 (they add up to 180°). Given that \( m \angle DAB = 124^\circ \), we can determine the other angles as follows:
1. **Find \( m \angle ABC \)**:
Adjacent angles in a rhombus are supplementary:
\[
m \angle ABC = 180^\circ - m \angle DAB
\]
\[
m \angle ABC = 180^\circ - 124^\circ = 56^\circ
\]
2. **Find \( m \angle BCD \)**:
Since opposite angles in a rhombus are equal,
\[
m \angle BCD = m \angle DAB = 124^\circ
\]
3. **Find \( m \angle CDA \)**:
Similarly, since opposite angles are equal,
\[
m \angle CDA = m \angle ABC = 56^\circ
\]
To summarize:
- \( m \angle DAB = 124^\circ \)
- \( m \angle ABC = 56^\circ \)
- \( m \angle BCD = 124^\circ \)
- \( m \angle CDA = 56^\circ \)
1. **Find \( m \angle ABC \)**:
Adjacent angles in a rhombus are supplementary:
\[
m \angle ABC = 180^\circ - m \angle DAB
\]
\[
m \angle ABC = 180^\circ - 124^\circ = 56^\circ
\]
2. **Find \( m \angle BCD \)**:
Since opposite angles in a rhombus are equal,
\[
m \angle BCD = m \angle DAB = 124^\circ
\]
3. **Find \( m \angle CDA \)**:
Similarly, since opposite angles are equal,
\[
m \angle CDA = m \angle ABC = 56^\circ
\]
To summarize:
- \( m \angle DAB = 124^\circ \)
- \( m \angle ABC = 56^\circ \)
- \( m \angle BCD = 124^\circ \)
- \( m \angle CDA = 56^\circ \)