Question

In parallelogram HIJK, the measure of angle J is 58 degrees. Draw a picture and complete the following: Find measure of angle H. Explain how you know. Find the measure of angle K. Explain how you know.

Answer 1

Measure of angle H: 58 degrees

Measure of angle K: 122 degrees

Knowing that angle J is 58 degrees in parallelogram HIJK, we can deduce that angle H is also 58 degrees because opposite angles in a parallelogram are equal. Angle K, being adjacent to angle J, must be supplementary to it, making it 122 degrees since adjacent angles in a parallelogram sum to 180 degrees.

To find the measures of angles H and K:

- In a parallelogram, opposite angles are equal. Since angle J is 58 degrees, angle H, being opposite to angle J, is also 58 degrees.

- Adjacent angles in a parallelogram are supplementary, meaning they add up to 180 degrees. Therefore, to find the measure of angle K, we subtract the measure of angle J from 180 degrees.

Let's calculate the measure of angle K

- Measure of angle H: 58 degrees

- Measure of angle K: 122 degrees

Knowing that angle J is 58 degrees in parallelogram HIJK, we can deduce that angle H is also 58 degrees because opposite angles in a parallelogram are equal. Angle K, being adjacent to angle J, must be supplementary to it, making it 122 degrees since adjacent angles in a parallelogram sum to 180 degrees.