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?

Answer 1

a) Yes, the sum of the two acute angles may be less than a right angle e.g. ${30}^{\circ }$ and ${45}^{\circ }$ are acute angles and their sum (i.e. ${30}^{\circ }+{45}^{\circ }={75}^{\circ }$ )is also an acute angle.

b) Yes, the sum of two acute angles may be equal to a right angle. e.g. ${30}^{\circ }+{60}^{\circ }={90}^{\circ }$

c) Yes, the sum of two acute angles may be more than a right angle, i.e. obtuse angle. e.g. ${60}^{\circ }+{70}^{\circ }={130}^{\circ }$

d) No, the sum of two acute angles is always less than a straight angle, i.e. ${180}^{\circ }$.

e) No, the sum of two acute angles is always less than ${180}^{\circ }$. So their sum cannot be a reflex angle.