The figure below is a rhombus Find the measure of angle 1.

Question

Answer 1

The diagonals of a rhombus bisect pairs of opposite angles, so that measure of that full upper corner angle is 64*2 = 128 degrees.

Consecutive angles of a parallelogram are supplementary so the measure of the full lower corner angle containing angle 1 is 180-128 = 52 degrees and the measure of angle 1, which is a bisected angle of that corner, is 26 degrees.