Question

1. find the measure of ∠2.

26°
52°
128°

Explanation:

Step1: Identify congruent triangles

The figure shows two triangles formed by the diagonal of a parallelogram - like shape. The marks on the sides indicate that the two triangles are congruent (by Side - Side - Side congruence criterion).

Step2: Use angle - congruence property

Corresponding angles of congruent triangles are equal. The angle of $26^{\circ}$ and $\angle1$ are corresponding angles of congruent triangles, so $\angle1 = 26^{\circ}$.

Step3: Use properties of parallelogram - adjacent angles

In a parallelogram, adjacent angles are supplementary. Let's assume the figure is a parallelogram. $\angle2$ and the angle composed of the $26^{\circ}$ angle and $\angle1$ are adjacent angles. The sum of adjacent angles in a parallelogram is $180^{\circ}$. But we can also use the fact that alternate - interior angles are equal. Since the figure likely represents a parallelogram, $\angle2$ and the $26^{\circ}$ angle are alternate - interior angles. So $\angle2=26^{\circ}$.

Answer:

$26^{\circ}$