Final answer:
To solve for x in the isosceles trapezoid QRST, set the expressions for the base angles equal to each other and solve the resulting equation. The correct value of x is 9.
Step-by-step explanation:
In an isosceles trapezoid QRST, the two base angles are given as (9x - 17)° and (4x + 28)°. We can find the value of x by using the property that in an isosceles trapezoid, the base angles are equal. This means that the expressions for the two base angles should be set equal to each other to solve for x.
Setting the expressions for the base angles equal to each other, we have:
9x - 17 = 4x + 28
Subtracting 4x from both sides, we get:
5x - 17 = 28
Adding 17 to both sides, we have:
5x = 45
Dividing both sides by 5, we get:
x = 9
Therefore, the correct answer is (a) x = 9.