Mathematics 10 — Exercise 9.2 · Q3 (ii), x

Full question

PQ is a diameter and QPR=38°. Find x=PQR.

OPQR∠QPR=38°x=PQR; y=PRQDiagram not to scale

Step-by-step solution

  1. A radius is perpendicular to the tangent at its point of contact, so the contact angle is 90°.

  2. The three angles of a triangle add to 180°. Subtract both known angles.

  3. Calculate this operation before combining the remaining terms.

    (-1)×90=-90

  4. Calculate this operation before combining the remaining terms.

    (-1)×38=-38

  5. Substitute the given numbers into the formula.

    180−90−38

  6. Calculate this operation before combining the remaining terms.

    180−90−38=52

  7. The required result is shown below. Unit: °

    52

Answer

The final answer is shown below.

52