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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
  
  Share
  
  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°
explanation: The provided text is a solution to a math problem from a chapter on the angle properties of circles. It contains a question with two parts (a) and (b), and the corresponding answers for each part.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: • 0
  Guru
  
  # 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.
  
  • 0
  
  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
  
  Share
  
  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°
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a solution to a math problem from a chapter on the angle properties of circles. It contains a question with two parts (a) and (b), and the corresponding answers for each part.
  
  Label: question-and-answer