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△ABC is an isosceles triangle with m∠A=20° and AB = AC. D and E are points on AB and AC such that AD = AE. I is the midpoint of the segment DE
If BD = ID, then the angles of △IBC are
  • a)
    110°, 35°, 35°
  • b)
    100°, 40°, 40°
  • c)
    80°, 50°, 50°
  • d)
    90°, 45°, 45°
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
△ABC is an isosceles triangle with m∠A=20° and AB = AC. D and E are p...
In △ABC,
m∠ABC = m∠ACB = ½ (180° - 20°) = 80°
Similarly in △ADE,
m∠ADE = m∠ADE = ½ (180° - 20°) = 80°
m∠ADE = m∠DBI + m∠DIB = 2 m∠DBI [ triangle BDI is isoceles]
Therefore, m∠DBI = 400
Hence, m∠IBC = m∠ABC - m∠DBI = 40°
Similarly, m∠ICB = 40°
Therefore, in △IBC,
m∠BIC = 100o
Hence, option b is a correct answer
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