Mathematics 10 — Exercise Review · Q4, a

Full question

ML is tangent at L, O,C,M are collinear, and LMC=22°. Find a=LOC.

OLCM∠LMC=22°a=LOC; b=OLC; c=LCODiagram 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)×22=-22

  5. Substitute the given numbers into the formula.

    180−90−22

  6. Calculate this operation before combining the remaining terms.

    180−90−22=68

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

    68

Answer

The final answer is shown below.

68