Answer:
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
