Questions: The image contains a geometric shape, specifically a rhombus (or diamond-shaped quadrilateral). The vertices are labeled A, B, C, and D. One of the angles is marked as 35°, and one of the sides is labeled "11x + 11".

Solution Steps

A rhombus is a type of quadrilateral where all four sides are of equal length. Additionally, the diagonals of a rhombus bisect each other at right angles (90 degrees).

In the given rhombus ABCD:

• \( \angle ACB = 35^\circ \)
• \( \angle ABD = 11x + 11 \)

Since the diagonals of a rhombus bisect each other at right angles, the angles formed at the intersection of the diagonals are 90 degrees. Therefore, the angles around point B (where the diagonals intersect) must sum to 180 degrees.

Given:

• \( \angle ACB = 35^\circ \)
• \( \angle ABD = 11x + 11 \)

Since \( \angle ACB \) and \( \angle ABD \) are adjacent angles around point B, they must sum to 90 degrees: \[ \angle ACB + \angle ABD = 90^\circ \] \[ 35^\circ + (11x + 11) = 90^\circ \]

\[ 35 + 11x + 11 = 90 \] \[ 11x + 46 = 90 \] \[ 11x = 90 - 46 \] \[ 11x = 44 \] \[ x = \frac{44}{11} \] \[ x = 4 \]

Final Answer