Question

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Answer 1

Answer:

(i) a) 90°

(ii) b) 72°

Explanation:

(i) Let us consider ABC as a triangle

Since AC is a diameter with O as centre then OA = OB = OC as all are radii of the same circle

We know,

∠ABO = ∠A      (OA = OB)

and ∠OBC = ∠C      (OB = OC)

∠ABC = ∠ABO + ∠OBC = ∠A + ∠C

From angle sum property of triangles:

∠A + ∠C + ∠ABC = 180

∠ABC + ∠ABC = 180

2∠ABC = 180

∠ABC = 180/2 = 90

(ii) From opposite angle sum property of cyclic quadrilaterals:

∠BCD + ∠A = 180

∠BCD = 180 - ∠A = 180 - 108 = 72