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To prove the exterior angle theorem, a line CE is drawn through C parallel to BA, as shown. Which angle is ∠ECD equal to?

Class 9Exterior Angle of a TriangleGeometry — Lines and Angles
  • A∠ACB (vertically opposite)
  • B∠BAC (alternate angles)
  • C∠ABC (corresponding angles)
  • D∠ACE (linear pair)

Step-by-Step Solution

BD is a transversal to the parallel lines BA and CE, so ∠ECD and ∠ABC are corresponding angles. (∠ACE = ∠BAC is the alternate-angle step, using AC as transversal.)
Answer: C) ∠ABC (corresponding angles)

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Through C a line CE is drawn parallel to BA, as shown. ∠ACE = 50° and ∠ECD = 55°. Find…In △ABC, ∠B = 45° and ∠C = 75°. Side CA is produced beyond A. What is the exterior angle…In the figure, D lies on BC. ∠BAD = 30°, ∠B = 45° and ∠C = 50°. Find ∠DAC.In △ABC, ∠B = 60° and ∠C = 40°. AD bisects ∠A and meets BC at D. Find ∠ADC.The exterior angles at B and C of △ABC add up to 250°. Find ∠A.