(6) In the diagram, QS is a diameter of the circle. Find the value of x + y.

140 degrees

Step-by-step explanation:

Let's say the angle right next to P is called a and the angle right next to S, not including y, is b. Next, the angle inside the quadrilateral but part of x is c and the angle inside the quadrilateral but part of the triangle is called d, as shown in the picture.

We are mainly interested in c, d, and y.

For quadrilateral QPTS:

- It is a quadrilateral, so all angles add up to 360 degrees

- Every vertex is on the circle's circumference, so it forms a cyclic quadrilateral, where opposite angles add up to 180 degrees

Given these, we can say that:

a + b + c + 130 = 360

a + b = 180

130 + c = 180

We are looking for c, so subtract 130 from both sides

c = 50

Triangle QRS:

- is a triangle, so the angles add up to 180 degrees

d + y + 90 = 180

subtract 90 from both sides to isolate d/y

d + y = 90

We know that c = 50, and d+c=x, so we can add c to both sides to get

d + c + y = 90 + 50 = 140

x + y = 140

Step-by-step explanation:

it would be 6xy and -16xy.