SQRT is a parallelogram. If m∠STR = 106°, which of the following statements is true?
quadrilateral SQRT has diagonals QT and SR that intersect at point U
m∠RTU = 53°
m∠QUR = 74°
m∠QST = 106°
m∠RQS = 106°
m∠RQS = 106° :)
If SQRT is a parallelogram and m∠STR = 106°, then we can determine the following statements:
1. The opposite angles in a parallelogram are congruent, so m∠RQS = m∠STR = 106°.
2. The diagonals of a parallelogram bisect each other, so point U is the intersection of diagonals QT and SR.
3. The opposite angles formed by the diagonals in a parallelogram are congruent, so m∠RTU = m∠QUR.
Therefore, the correct statement is: m∠RTU = m∠QUR.
To find the correct statement, we need to use the given information about angle STR being 106°. We also know that SQRT is a parallelogram, which means opposite angles are congruent.
Let's apply this information to the given statements:
Statement 1: "quadrilateral SQRT has diagonals QT and SR that intersect at point U."
This statement does not directly provide any information about the angles in the parallelogram, so it is not relevant to our question.
Statement 2: "m∠RTU = 53°."
This angle is not directly related to the given angle STR, so it cannot be determined to be true based on the information provided.
Statement 3: "m∠QUR = 74°."
Since SQRT is a parallelogram, the opposite angles must be congruent. Therefore, if m∠STR = 106°, then m∠QST (which is opposite angle STR) must also be 106°. This statement is not true.
Statement 4: "m∠RQS = 106°."
Similarly to statement 3, if m∠STR = 106°, then m∠RQS (which is also opposite angle STR) must also be 106°. Therefore, this statement is true.
In conclusion, the correct statement is: "m∠RQS = 106°."