Answer:
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
[tex] = > 90 + x = 120[/tex]
[tex] = > x = 120 - 90 = 30[/tex]
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
[tex] = > 90 + y + y = 180[/tex]
[tex] = > 2y = 180 - 90 = 90[/tex]
[tex] = > y = \frac{90}{2} = 45[/tex]
