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Z.11 Find missing angles in quadrilaterals II
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A parallelogram has one angle that measures . What are the measures of the other three angles in the parallelogram?
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Ask by Bush Simmons. in the United States
Mar 22,2025

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Tutor-Verified Answer

Answer

All four angles in the parallelogram are .

Solution

  1. In any parallelogram, opposite angles are equal and consecutive angles are supplementary (i.e., they add up to ).
  2. Since one angle is given as , its consecutive angles must satisfy
    which gives
  3. The angle opposite the given is also .
  4. Therefore, all four angles in the parallelogram are .
The measures of the other three angles are , , and .

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Beyond the Answer

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (they add up to ). So, if one angle measures , the opposite angle will also measure . The two adjacent angles will each measure since , thus making the missing angles also .
Think of a parallelogram as a type of rectangle for this problem! The unique property of parallelograms means that if one angle is , all angles are effectively . So, it’s not just an angle-checking exercise; you’ve ended up with a square! How fun is that?

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