Quadrilateral PQRS is shown.There is a quadrilateral PQRS in which the length of side PQ is 6b, the length of side QR is 4a+1, the length of side RS is 11b-10, and the length of side PS is 2a+9. The measure of angle PQR is (6x+13) degrees and the measure of angle PSR is (7x-5) degrees.What must the values of a and b be for PQRS to be a parallelogram?
Accepted Solution
A:
Answer:The value of a = 8 and b= 2 for PQRS to be a parallelogram Step-by-step explanation:Given as :Quadrilateral PQRS having side PQ , QR , RS , PSThe measure of side is PQ = 6b , QR = 4a + 1RS = 11b - 10 , PS = 2a + 9The measure of angle PQR is (6x + 13) And PSR is (7x - 5)The parallelogram become quadrilateral when its opposite sides is parallel and equal I.e PQ = RS And QR = PSOr 6b = (11b - 10) Or, 10 = 11b - 6b Or, 5b = 10 ∴ b= [tex]\frac{10}{5}[/tex] = 2 or, b = 2Again ∵ QR = PSSo, 4a + 1 = 2a + 9Or, 4a - 2a = 9 - 1∴ a = 8Hence the value of a = 8 and b= 2 for PQRS to be a parallelogram Answer