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? (5 x 0.5 marks = 2.5 marks)
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? (5 x 0.5 marks = 2.5 marks)
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.
(5 x 0.5 marks = 2.5 marks)
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.
(5 x 0.5 marks = 2.5 marks)
