SQRT is a parallelogram. If m∠QST = 72°, which of the following statements is true?
quadrilateral SQRT has diagonals QT and SR that intersect at point U
m∠SQR = 72°
m∠QRT = 72°
m∠QSR = 36°
m∠TRQ = 108°
whats the answer
To determine which of the given statements is true, we need to use the properties of a parallelogram.
First, let's understand the angles in a parallelogram. In a parallelogram, opposite angles are congruent, which means they have the same measure. Additionally, adjacent angles are supplementary, meaning they add up to 180°.
Given that SQRT is a parallelogram and m∠QST = 72°, we can determine the following:
1. m∠QSR = 180° - m∠QST (adjacent angles are supplementary)
m∠QSR = 180° - 72°
m∠QSR = 108°
2. Opposite angles in a parallelogram are congruent, so m∠SQR = m∠TRQ.
Now, let's check each of the given statements against our findings:
A. m∠SQR = 72°: This statement is not true because we found that m∠SQR = m∠TRQ = 108°.
B. m∠QRT = 72°: This statement is not true. We haven't determined the measure of angle QRT.
C. m∠QSR = 36°: This statement is not true either. We found that m∠QSR = 108°.
D. m∠TRQ = 108°: This statement is true based on our conclusions. We determined that m∠TRQ = m∠SQR = 108°.
Therefore, the correct statement is: m∠TRQ = 108°.
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U has nothing to do with anything.
Adjacent angles of a parallelogram are supplementary.