Question

question
answer attempt 2 out of 3
ab || dc
x = 12

Explanation:

Step1: Identify the relationship

Since \( AB \parallel DC \) and \( AD \) is a transversal, \( \angle A \) and \( \angle D \) are same - side interior angles, so they are supplementary. But also, in a parallelogram (since \( AB\parallel DC \) and \( AD \) and \( BC \) are sides, if we assume it's a parallelogram, adjacent angles are supplementary, but also, if we look at the figure, \( \angle A \) and \( \angle D \) can also be equal if it's a rectangle? Wait, no, wait. Wait, in the figure, \( AB \parallel DC \) and \( AD \) is a side. Wait, actually, if \( AB \parallel DC \) and \( AD \) is perpendicular? No, wait, the angles at \( A \) and \( D \): if we consider that \( AB \parallel DC \) and \( AD \) is a transversal, then \( \angle A+\angle D = 180^{\circ}\)? Wait, no, maybe it's a parallelogram, so \( \angle A=\angle D \)? Wait, no, in a parallelogram, opposite angles are equal, adjacent angles are supplementary. Wait, but the problem has \( \angle A = 11x^{\circ}\) and \( \angle D=10x + 12^{\circ}\). Wait, maybe it's a rectangle, so \( \angle A=\angle D = 90^{\circ}\)? No, that can't be. Wait, maybe I made a mistake. Wait, if \( AB \parallel DC \) and \( AD \) is a side, and if the figure is a parallelogram, then \( \angle A+\angle D=180^{\circ}\)? No, adjacent angles in a parallelogram are supplementary. But maybe the figure is a rectangle, so \( \angle A=\angle D = 90^{\circ}\), but that would mean \( 11x=10x + 12\), so \( x = 12\). Ah, that makes sense. So we set \( 11x=10x + 12\) because in a rectangle (or if \( AD \) is perpendicular to \( AB \) and \( DC \)), the angles at \( A \) and \( D \) are right angles, so they are equal.

Step2: Solve for \( x \)

Set \( 11x=10x + 12\)
Subtract \( 10x \) from both sides: \( 11x-10x=10x + 12-10x\)
Which gives \( x = 12\)

Answer:

\( x = 12\)