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Given: ∠A=36° and ∠B=64°

To find: The longest and shortest sides of the triangle

Given that ∠A=36° and ∠B=64°

Hence, by the angle sum property in ∆ABC, we have

∠A + ∠B + ∠C = 180°

36° + 64°+ ∠C = 180°

100° + ∠C = 180°

∠C = 80°

So, we have ∠A=36°, ∠B=64° and ∠C = 80°

∴∠C is largest and ∠A is shortest

Hence,

Side opposite to ∠C is longest.

∴AB is longest

Side opposite to ∠A is shortest.

∴ BC is shortest