Question

Sqrt is a parallelogram. if ?sqr = 108�, which of the following statements is true? quadrilateral sqrt has diagonals qt and sr that intersect at point u ?squ = 72� ?qrt = 108� ?qst = 72� ?rqu = 54�

Answer 1

Among the given statements, m ∠SQU = 72∘ is true.

Since SQRT is a parallelogram, opposite angles are equal, and consecutive angles are supplementary. Given that m ∠SQR=108∘ , we can determine the following:

1. m ∠QRT is equal to m ∠SQR since they are opposite angles in a parallelogram. Therefore, m ∠QRT=108∘ .

2. m ∠QST is supplementary to m ∠SQR, so m ∠QST = 180∘ −108∘ = 72∘ .

3. m ∠SQU is also supplementary to m ∠SQR, so m ∠SQU = 180∘ − 108∘ =72∘ .

4. m ∠RQU is equal to m ∠SQR since they are opposite angles in a parallelogram. Therefore, m ∠RQU = 108∘ .

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