Can we have two acute angles whose sum is
(a) an acute angle? (b) a right angle? (c) an obtuse angle? (d) a straight angle? (e) a reflex angle?
(a) Yes; e.g., \(20^{\circ}+30^{\circ}=50^{\circ}\) (acute).
(b) Yes; e.g., \(30^{\circ}+60^{\circ}=90^{\circ}\).
(c) Yes; e.g., \(50^{\circ}+60^{\circ}=110^{\circ}\) (obtuse).
(d) No; sum of two acute angles is \(<180^{\circ}\).
(e) No; a reflex angle is \(>180^{\circ}\), impossible with two acute angles.
Each acute angle is \(<90^{\circ}\); hence their sum can be \(<180^{\circ}\) and may equal \(90^{\circ}\) or lie between \(90^{\circ}\) and \(180^{\circ}\) but cannot reach or exceed \(180^{\circ}\).