In a rhombus, the difference of the measures of the two angles between a side and the diagonals is 32°. What are the measures of the angles of the rhombus?

Question

Please help me. I don't understand what the question means.

Answer 1

It sounds a little ambiguous but...

draw a rhombus and its diagonals

you have 4 triangles

look at the top one

some facts about a rhombus...

the diagonals intersect at right angles

the diagonals bisect the angles

consecutive angles are supplementary

opposite angles are congruent

in the triangle the angle where the diagonals intersect is a 90º angle

the other two interior angles, which are the angles you are talking about, must add up to 90º

call one x and call the other x+32

x+x+32=90

2x+32=90

2x=90-32

2x=58

x=58/2

x=29º

x+32=61º

now double each angle because the diagonal bisected each angle

2*29=58º

2*61=122º

the opposite angles are congruent so the other two angles are 58º and 122º also