Question

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​

Answer 1

a). m∠a = 62°

b). m∠b = 118°

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°