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At most how many of the three exterior angles of a triangle (one at each vertex) can be acute?

Class 9Exterior Angle of a TriangleGeometry — Lines and Angles
  • A3
  • B2
  • C0
  • D1

Step-by-Step Solution

An acute exterior angle means an obtuse interior angle, and a triangle has at most one obtuse angle. So at most one exterior angle is acute.
Answer: D) 1

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To prove the exterior angle theorem, a line CE is drawn through C parallel to BA, as…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.