The key here is to know that a rhombus has two pairs of congruent angles. In other words, the two acute angles of a rhombus are equal and the two obtuse angles are equal. 

In this problem, since the two acute angles add up to \(\displaystyle \small 60^{o}\) and they must both be the same amount, each of the acute angles must be \(\displaystyle \small 30^{o}\).

It is also important to know that the four angles of a rhombus add up to \(\displaystyle \small 360^{o}\). If the two acute angles add up to \(\displaystyle \small 60^{o}\), then that means that the two obtuse angles must add up to \(\displaystyle \small 360^{o}-60^{o}\), or \(\displaystyle \small 300^o\).

Finally, because the obtuse angles add up to \(\displaystyle \small 300^o\) and they must be congruent, each of the obtuse angles must be \(\displaystyle \small 150^{o}\).

First, consider that the sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\). 

One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with \(\displaystyle 146$^\circ$\).  Find the difference between \(\displaystyle 180$^\circ$\) and \(\displaystyle 146$^\circ$\) to find the solution. 

The correct answer is: 

\(\displaystyle 180-146=34$^\circ$\)

A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\).

If a rhombus has an interior angle that has a measurement of \(\displaystyle 73$^\circ$\), the adjacent angle must equal: 

\(\displaystyle 180-73=107$^\circ$\)
 

 The sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\).

Since, two of the opposite interior angles in this rhombus have a sum measurement of \(\displaystyle 158$^\circ$\), the sum of the remaining two angles must equal:

\(\displaystyle 360-158=202$^\circ$\)

To check your answer note: 

\(\displaystyle 202+158=360\) (meaning the sum of the four interior angles equals \(\displaystyle 360$^\circ$\)).

 A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\).

Since this problem involves supplementary angles, the solution is: 

\(\displaystyle 97+25+x=180\)

\(\displaystyle 122+x=180\)

\(\displaystyle x=180-122=58$^\circ$\)

The sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\). 

One way to approach this problem is to realize that each of the remaining two angles must have the same measurement, and that each will be supplementary angles with \(\displaystyle 68$^\circ$\).

Find the difference between \(\displaystyle 180$^\circ$\) and \(\displaystyle 68$^\circ$\) to find the solution. 

\(\displaystyle 180-68=112$^\circ$\)

To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\). 

Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from \(\displaystyle 360$^\circ$\) to find the sum of the two remaining interior angles. 

The solution is: 

\(\displaystyle 75+75=150\)

\(\displaystyle 360-150=210$^\circ$\)

To solve this problem, consider that the sum total of the four interior angles in any rhombus must equal \(\displaystyle 360$^\circ$\). Furthermore, a rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\). 

Since this problem provides the measurement for two of the interior angles, find the sum of those two angles. Then subtract that sum from \(\displaystyle 360$^\circ$\) to find the sum of the two remaining interior angles. 

The solution is: 

\(\displaystyle 129+129=258\)

\(\displaystyle 360-258=102$^\circ$\)

A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\).

Therefore, if a rhombus has an interior angle that has a measurement of \(\displaystyle 140$^\circ$\), then the adjacent angle must equal: 

\(\displaystyle 180-140=40$^\circ$\)

 A rhombus must have two sets of equivalent opposite interior angles, and a rhombus must have two sets of adjacent interior angles. The adjacent interior angles must be supplementary—meaning they have a sum total of \(\displaystyle 180$^\circ$\).

Since this problem involves supplementary angles, the solution is: 

\(\displaystyle 180-84=96$^\circ$\)

Check answer by:

\(\displaystyle 96+84=180$^\circ$\)