Question

1. find the measure of ∠1.

104°
76°
104°
38°

Explanation:

Step1: Recall parallelogram property

In a parallelogram, adjacent - angles are supplementary. Let the parallelogram be \(ABCD\) with \(\angle B = 104^{\circ}\). Then \(\angle A+\angle B=180^{\circ}\). Also, the diagonal of a parallelogram bisects the angles of the parallelogram.

Step2: Calculate half - of adjacent angle

Since the diagonal of the parallelogram divides the angle at the vertex, and the adjacent angle to the \(104^{\circ}\) angle is \(180 - 104=76^{\circ}\). The diagonal bisects this adjacent angle.
So, \(\angle1=\frac{180 - 104}{2}\).
\[

$$\begin{align*} \angle1&=\frac{76}{2}\\ & = 38^{\circ} \end{align*}$$

\]

Answer:

\(38^{\circ}\)