Find the measurements of the unknown angles in this figure

x = 30° ; y = 45°

Step-by-step explanation:

Angle subtended by the diameter on any point of the circle is 90°. So,angleRSP = 90°

angleRST = 120° (given)

But,

angleRST = angleRSP + anglePST

In triangle PQR , PQ = RQ (given)

Hence , it is an isosceles triangle. As it is an isosceles triangle , the base angles are equal.

=> anglePRQ = angleRPQ = y°

anglePQR = 90° (Angle subtended by diameter on any point of circle is 90°)

According to Angle Sum Property of Triangle,

anglePRQ + angleRPQ = anglePQR

step-by-step explanation:

for exempl this   system of equations   y = x - 3

                                                                y = 2x - 5

look   the line : y = x -3     ( red)

                            the line : y = 2x -5 ( bleus)