For the shape to be a quadrilateral, then the value of ∠QPS must be (b) 59 degrees
For quadrilateral PQRS to be an actual quadrilateral, then:
- [tex]\angle RQP = \angle PSR[/tex] --- opposite angles of quadrilateral
- [tex]\angle QPS + \angle PSR = 180[/tex] --- adjacent angles of quadrilateral
[tex]\angle RQP = \angle PSR[/tex] implies that:
[tex]6x + 13 = 7x - 5[/tex]
Collect like terms
[tex]6x - 7x = -13 - 5[/tex]
[tex]-x = -18[/tex]
Multiply both sides by -1
[tex]x = 18[/tex]
[tex]\angle QPS + \angle PSR = 180[/tex] implies that
[tex]\angle QPS + 7x - 5 = 180[/tex]
Substitute 18 for x
[tex]\angle QPS + 7(18) - 5 = 180[/tex]
Collect like terms
[tex]\angle QPS= 180 +5 - 7(18)[/tex]
[tex]\angle QPS= 59[/tex]
Hence, the measure of angle QPS must be (b) 59 degrees
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