Question
In the diagram above, quadrilateral ABCD is a rhombus. If the m DAB= 124 degrees find the measurements below.
Answers
Answered by
GPT-4o mini
In a rhombus, opposite angles are equal, and consecutive angles are supplementary. Given that \( m \angle DAB = 124^\circ \), we can find the other angles as follows:
1. Since \( \angle DAB \) and \( \angle ABC \) are consecutive angles in the rhombus, they sum to \( 180^\circ \):
\[
m \angle ABC = 180^\circ - m \angle DAB = 180^\circ - 124^\circ = 56^\circ.
\]
2. Since opposite angles are equal in a rhombus:
\[
m \angle BCD = m \angle DAB = 124^\circ,
\]
and
\[
m \angle CDA = m \angle ABC = 56^\circ.
\]
Thus, the measures of the angles in rhombus ABCD are:
- \( m \angle DAB = 124^\circ \)
- \( m \angle ABC = 56^\circ \)
- \( m \angle BCD = 124^\circ \)
- \( m \angle CDA = 56^\circ \)
If you need any further calculations or clarifications, let me know!
1. Since \( \angle DAB \) and \( \angle ABC \) are consecutive angles in the rhombus, they sum to \( 180^\circ \):
\[
m \angle ABC = 180^\circ - m \angle DAB = 180^\circ - 124^\circ = 56^\circ.
\]
2. Since opposite angles are equal in a rhombus:
\[
m \angle BCD = m \angle DAB = 124^\circ,
\]
and
\[
m \angle CDA = m \angle ABC = 56^\circ.
\]
Thus, the measures of the angles in rhombus ABCD are:
- \( m \angle DAB = 124^\circ \)
- \( m \angle ABC = 56^\circ \)
- \( m \angle BCD = 124^\circ \)
- \( m \angle CDA = 56^\circ \)
If you need any further calculations or clarifications, let me know!