If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.
Question:

If the base of an isosceles triangle is produced on both sides, prove that the exterior angles so formed are equal to each other.

Solution:

ED is a straight line segment and B and C an points on it.

∠EBC = ∠BCD = straight angle = 180°

∠EBA + ∠ABC = ∠ACB + ∠ACD

∠EBA = ∠ACD + ∠ACB – ∠ABC

∠EBA = ∠ACD [From (i) ABC = ACD]

∠ABE = ∠ACD

Hence proved

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