Question

find the measures of the numbered angles in the rhombus.
m∠1=□°

Explanation:

Step1: Recall rhombus diagonal properties

The diagonals of a rhombus bisect the interior angles, and they are perpendicular to each other (so $\angle 2 = 90^\circ$). Also, opposite angles of a rhombus are equal, and adjacent angles are supplementary.

Step2: Find $\angle 1$ using right triangle

In the right triangle formed by the diagonals, we know one acute angle is $26^\circ$. The sum of angles in a triangle is $180^\circ$, so:
$\angle 1 = 90^\circ - 26^\circ$

Step3: Calculate the value

$\angle 1 = 64^\circ$

Answer:

$64$