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Question

# Can we have two acute angles whose sum is a) an acute angle? Why or Why not? b) a right angle? Why or Why not? c) an obtuse angle? Why or Why not? d) a straight angle? Why or Why not? e) a reflex angle? Why or Why not?

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Solution

## a) Yes, the sum of the two acute angles may be less than a right angle e.g. 30∘ and 45∘ are acute angles and their sum (i.e. 30∘+45∘=75∘ )is also an acute angle. b) Yes, the sum of two acute angles may be equal to a right angle. e.g. 30∘+60∘=90∘ c) Yes, the sum of two acute angles may be more than a right angle, i.e. obtuse angle. e.g. 60∘ + 70∘ = 130∘ d) No, the sum of two acute angles is always less than a straight angle, i.e. 180∘. e) No, the sum of two acute angles is always less than 180∘. So their sum cannot be a reflex angle.

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