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Ques 7 (b) In the figure given below, if ∠ACE = 43° and ∠CAF = 62°, find the values of a, b and c

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This is an important and exam oriented question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

This question has been asked in previous year question paper of 2007

 

In the figure given,  ∠ACE = 43° and ∠CAF = 62°,we have to  find the values of a, b and c Avichal publication
Understanding ICSE Mathematics
Question 7(b)

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1 Answer

  1. In the given figure,

    ∠ACE 43and ∠CAF = 620

    Now, in ∆AEC

    ∠ACE + ∠CAE + ∠AEC = 180o

    43+ 62+ ∠AEC = 180o

    105+ ∠AEC = 180o

    ∠AEC = 180– 105= 75o

    But ∠ABD + ∠AED = 1800

    (sum of opposite angles of acyclic quadrilateral)

    and ∠AED = ∠AEC

    a + 75= 180o

    a = 180– 75– 105o

    but ∠EDF = ∠BAE

    (Angles in the alternate segment)

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