There is a rhombus with 4 points, top left A, top right B, bottom leftt D, and bottom right C, with a diagonal line in the middle

Question

In the diagram of a rhombus ABCD, mA=112. What is mADB?

mADB=____

Answer 1

To find the measure of angle \( ADB \) in rhombus \( ABCD \), we can use the properties of rhombuses and triangles.

1. In a rhombus, the opposite angles are equal, and the adjacent angles are supplementary. Since \( mA = 112^\circ \), we know: \[ mC = 112^\circ \]

2. The adjacent angles \( A \) and \( B \) are supplementary: \[ mA + mB = 180^\circ \] Therefore, we can find \( mB \): \[ mB = 180^\circ - 112^\circ = 68^\circ \] Similarly, since \( mC \) and \( mD \) are also adjacent: \[ mC + mD = 180^\circ \] Thus, \[ mD = 180^\circ - 112^\circ = 68^\circ \]

3. The diagonals of a rhombus bisect each other at right angles. Therefore, triangle \( ADB \) is formed by the diagonal \( DB \), where \( D \) is the bottom left vertex.

4. Since diagonals bisect the angles of the rhombus, we can find \( mADB \): \[ mADB = \frac{mA}{2} = \frac{112^\circ}{2} = 56^\circ \]

So, the measure of angle \( ADB \) is: \[ mADB = 56^\circ \]

Answer 2

it isn't 56

Answer 3

I apologize for any misunderstanding in my previous answer. Let's correctly analyze the situation regarding rhombus ABCD with \( \angle A = 112^\circ \) and find \( m\angle ADB \) more clearly.

1. In rhombus \( ABCD \):

   • \( \angle A = 112^\circ \)
   • \( \angle C = 112^\circ \) (opposite angles are equal)
   • \( \angle B = 68^\circ \) and \( \angle D = 68^\circ \) (adjacent angles are supplementary)

2. The diagonals of a rhombus bisect the angles. Thus, each diagonal will split the vertex angles into two equal parts.

3. For \( \angle ADB \):

   • Since \( \angle A \) (which is at point A) measures \( 112^\circ \), when bisected, each half will measure \( 56^\circ \).

4. The interior angle \( \angle ADB \) consists of \( \angle A \) and \( \angle D \):

   • \( \angle ADB = \angle A + \angle D = 112^\circ + 68^\circ\)
   • But we want \( \angle ADB \) directly, not combining angles from \( A \) and \( D \).

In right triangle \( ADB\):

• \( \angle ADB\) is actually formed with vertex D.
• Since the diagonals bisect each other at right angles, we can observe that triangle \( ADB \) is formed by angles from diagonal \( DB \).

5. Therefore, \( \angle ADB \) is half of \( 68^\circ \) and equals \( 34^\circ \).

Thus, the measure of angle \( ADB \) is: \[ m\angle ADB = 34^\circ \]

Please accept my apologies for the confusion earlier, and thank you for your patience!

Answer 4

correct

Answer 5

Thank you for confirming! To summarize:

In rhombus \( ABCD \), where \( m\angle A = 112^\circ \), the calculation yields:

• \( m\angle B = 68^\circ \)
• \( m\angle D = 68^\circ \)

When finding \( m\angle ADB \):

• The diagonals bisect the angles of the rhombus. Since \( \angle A = 112^\circ \), \( m\angle ADB \) is half of \( \angle D = 68^\circ \).

So, the final answer is: \[ m\angle ADB = 34^\circ \]

If you have any further questions or need additional assistance, feel free to ask!