To solve the given problem:

Step 1: Understanding the properties of a parallelogram

In a parallelogram:

1. Opposite angles are equal.
2. Adjacent angles are supplementary, meaning their measures add up to $180^\circ$.

Step 2: Given information

• The measure of angle $H = 45^\circ$.

Step 3: Finding the measure of angle $J$

Since angle $H$ and angle $J$ are adjacent angles in the parallelogram, they are supplementary: $\text{Measure of angle } H + \text{Measure of angle } J = 180^\circ$ Substituting the given value: $45^\circ + \text{Measure of angle } J = 180^\circ$ $\text{Measure of angle } J = 180^\circ - 45^\circ$ $\text{Measure of angle } J = 135^\circ$

Step 4: Explanation

Angle $J$ measures $135^\circ$ because adjacent angles in a parallelogram are supplementary (their measures sum to $180^\circ$).

Would you like further clarification or details? Here are some follow-up questions:

1. What is the measure of the other two angles in the parallelogram?
2. Why do adjacent angles in parallelograms always sum to $180^\circ$?
3. How would this calculation change if the parallelogram were a rectangle?
4. What are some other properties of parallelograms that can be helpful in angle problems?
5. How would you find an angle if the parallelogram is irregular?

Tip: Always review the properties of shapes when solving geometry problems to identify helpful relationships!