In the centre o is the centre and ab is a diameter a) work out the value of angle a

b) work out the size of angle b

a). m∠a = 62°

b). m∠b = 118°

Step-by-step explanation:

a). Since, an angle inscribed in a semicircle is a right angle,

   m∠ACB = 90°

   By triangle sum theorem in ΔABC,

   m∠CAB + m∠ACB + m∠ABC = 180°

   28° + 90° + m∠ABC = 180°

   118° + m∠ABC = 180°

   m∠ABC = 180°- 118°

   a = 62°

b). Since, quadrilateral ABCD is a cyclic quadrilateral,

    m∠ADC + m∠ABC = 180°

    b + a = 180°

    b + 62° = 180°

    b = 180° - 62°

    b = 118°

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