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)
In the given figure,
∠ACE 43o and ∠CAF = 620
Now, in ∆AEC
∠ACE + ∠CAE + ∠AEC = 180o
43o + 62o + ∠AEC = 180o
105o + ∠AEC = 180o
∠AEC = 180o – 1050 = 75o
But ∠ABD + ∠AED = 1800
(sum of opposite angles of acyclic quadrilateral)
and ∠AED = ∠AEC
a + 75o = 180o
a = 180o – 75o – 105o
but ∠EDF = ∠BAE
(Angles in the alternate segment)