Question

"SQRT is a parallelogram. If m angle SQR = 108 degrees, which of the following statements is true

A: m angle SQU = 72 degrees
B: m angle QRT = 108 degrees
C: m angle QST = 72 degrees
D: m angle RQU = 54 degrees"

Answer 1

In a parallelogram like SQRT, opposite angles are equal and consecutive angles sum up to 180 degrees. Since m angle SQR is given as 108 degrees, m angle QRT, which is opposite to SQR, is also 108 degrees. Therefore, the true statement is Option B: m angle QRT = 108 degrees.

Step-by-step explanation:

The question involves the properties of a parallelogram, which in this case is SQRT. In a parallelogram, opposite angles are equal, and consecutive angles are supplementary (adding up to 180 degrees). Given that m angle SQR = 108 degrees, the angle adjacent to it, m angle SRQ, must be supplementary to it. Therefore, m angle SRQ = 180 degrees - 108 degrees = 72 degrees. Since SQRT is a parallelogram, its opposite angles are equal which means m angle SQR = m angle TQU and m angle SRQ = m angle TQS. With this information, we can conclude that Option B: m angle QRT = 108 degrees is true because angle QRT is opposite to angle SQR, and they must be equal.