Introduction to Parallelograms

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A parallelogram is a quadrilateral with two pairs of parallel sides. One of the key properties of a parallelogram is that opposite angles are equal and adjacent angles are supplementary (i.e., they add up to 180 degrees).

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Problem Statement

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The problem at hand is to determine the measures of the remaining angles in a parallelogram when one angle is given as 62 degrees.

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Solution

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Let's denote the parallelogram as ABCD.

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Given that A 62°.

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1. **Finding Angle C:**

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Since opposite angles in a parallelogram are equal, we have:

r r (angle C angle A 62°)r r

2. **Finding Angle B and D:**

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Adjacent angles in a parallelogram are supplementary, so:

r r (angle A angle B 180°)r r

Therefore, substituting the value of A:

r r (62° angle B 180°)r r

From this, we can solve for B:

r r (angle B 180° - 62° 118°)r r

Since opposite angles are equal, we have:

r r (angle D angle B 118°)r r

Verification

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To verify, we can sum up all the angles in the parallelogram, which should equal 360 degrees:

r r (angle A angle B angle C angle D 62° 118° 62° 118° 360°)r r

Conclusion

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The measures of the remaining angles in the parallelogram are 62° and 118°. Specifically:

r r r A C 62°r B D 118°r r r

Additional Insights

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Understanding the properties of parallelograms can help in solving more complex geometric problems. If you have any further questions or need assistance with other shape-related problems, feel free to ask.