In the diagram TS is a tangent to the circle at... - WAEC Mathematics 2016 Question

In the diagram above, x₁ = 180^o - 117^o = 63^o(opposite angles of a cyclic quad.)

x₁ = x₂ (base angles of isos. (\Delta))

x₁ + x₂ + (\alpha) = 180^o (sum of angles of a (\Delta)

63^o + 63^o + (\alpha) = 180^o

(\alpha) = 180^o - (63 + 63)^o

= 54^o