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  # Question 5. (a) In the figure (i) given below, ABCD is a parallelogram. A circle passes through A and D and cuts AB at E and DC at F. Given that ∠BEF = 80°, find ∠ABC. (b) In the figure (ii) given below, ABCD is a cyclic trapezium in which AD is parallel to BC and ∠B = 70°, find: (i)∠BAD (ii) DBCD.
  
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  This is circle based question from Chapter name- circles
  Topic – Angle properties of circles
  Chapter number- 15
  
  In this question we have been given the information about the angles and we have to find the value of angles asked in question.
  ICSE Avichal publication
  Understanding ICSE Mathematics
  Question no 5
  
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  1. Solution:
  Ext. ∠FEB = ∠ADF
  ⇒ ∠ADF = 80°
  ABCD is a parallelogram
  ∠B = ∠D = ∠ADF = 80°
  or ∠ABC = 80°
  (b)In trapezium ABCD, AD || BC
  (i) ∠B + ∠A = 180°
  ⇒ 70° + ∠A = 180°
  ⇒ ∠A = 180° – 70° = 110°