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Use the property that the radius is perpendicular to the tangent at the point of contact.

Mathematics

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Here are the calculations for each angle with reasons:

8.1.1 P^\hat{P}

  1. Use the property that the radius is perpendicular to the tangent at the point of contact.

    OM is a radius and TM is a tangent.

    ∠OMT=90∘\angle OMT = 90^\circ
  2. Calculate ∠OMR\angle OMR.

    Given M^1=∠TMR=66∘\hat{M}_1 = \angle TMR = 66^\circ.

    ∠OMR=∠OMT−∠TMR=90∘−66∘=24∘\angle OMR = \angle OMT - \angle TMR = 90^\circ - 66^\circ = 24^\circ
  3. Use the properties of an isosceles triangle.

    In △OMR\triangle OMR, OM = OR (radii of

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