Question

1) In the given figure, LABD = 54º and LBCD = 43°, calculate (i) LACD (ii) _BAD (iii)LBDA.

Answer 1

Step-by-step explanation:

(i) We know that the angles in the same segment of a circle are equal From the figure we know that ∠ABD and ∠ACD are in the segment AD ∠ABD = ∠ACD = 54o (ii) We know that the angles in the same segment of a circle are equal From the figure we know that ∠BAD and ∠BCD are in the segment BD ∠BAD = ∠BCD = 43o (iii) In △ ABD Using the angle sum property ∠BAD + ∠ADB + ∠DBA = 180o By substituting the values 43o + ∠ADB + 54o = 180o On further calculation ∠ADB = 180o – 43o – 54o By subtraction ∠ADB = 180o – 97o So we get ∠ADB = 83o It can be written as ∠BDA = 83o

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