Question

1. find the length of the two missing sides in the parallelogram below.
2. find the measure of the three missing angles in the parallelogram below.
3. find the measure of the three missing angles in the rhombus below.
4. find the length of the two missing sides in the parallelogram below.

Explanation:

Step1: Recall properties of parallelograms and rhombuses

In a parallelogram, opposite sides are equal and opposite angles are equal, and adjacent angles are supplementary (sum to 180°). A rhombus is a special - type of parallelogram with all sides equal.

Step2: Solve for angles in the rhombus (question 4)

Let the given angle in the rhombus be \(\theta = 38^{\circ}\).

• Opposite angle is equal, so one of the missing angles is also \(38^{\circ}\).
• Adjacent angles are supplementary. Let the adjacent angle be \(x\). Then \(x + 38^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-38^{\circ}=142^{\circ}\). The other adjacent angle (opposite to the first - found adjacent angle) is also \(142^{\circ}\).

Step3: Solve for sides in parallelograms (questions 1 and 5)

In a parallelogram, if one side is given, the opposite side has the same length. Since no side - lengths are given in the description, assume the side opposite to a given side \(a\) has length \(a\).

Answer:

For question 4: The three missing angles are \(38^{\circ},142^{\circ},142^{\circ}\).
For question 1 and 5: Without specific side - length values given in the problem, we can only say that the opposite sides of the parallelogram have the same length as their opposite counterparts. If a side length is \(s\), the opposite side has length \(s\).