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Mariana [72]
3 years ago
7

Find the measurements of the unknown angles in this figure

Mathematics
1 answer:
dem82 [27]3 years ago
3 0

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

=  > 90 + x = 120

=  > x = 120 - 90 = 30

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

=  > 90 + y + y = 180

=  > 2y = 180 - 90 = 90

=  > y =  \frac{90}{2}  = 45

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