Find the angel x in d diagram above with a well structured solution.

Step-by-step

Please refer to attached image.

1. Quad PQRS is cyclic (all vertices on the same circle), so opposite angles are supplementary, meaning

  that

  angles QPS and QRS are supplementary =>

  QPS+QRS=180   =>

  QRS = 180 - 74 = 106

2. Triangle RSQ is isosceles with RS=RQ =>

   angles RSQ and RQS are congruent.

3. Angle RSQ = (180 - 106) /2 = 74 / 2  = 37

4. QP is a diameter => angle QSP is a right-angle.

5. From (3) and (4) above,

  angle RSP = 37+90 = 127

6. Since PQRS is cyclic, angles RQP  and RSP are supplementary =>

   RQP+RSP = 180   =>

   x + 127 = 180   =>

   x = 180 - 127 = 53 degrees.

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step-by-step explanation: