Make an acute turn with the straws or fan. Continue to make another acute turn. Can the two acute turns together make another acute turn?

Question

Accepted Answer

Sometimes yes, and sometimes no. It depends on how big the two acute turns are. Try three cases with your straws. Two small acute turns. Turn a little, then a little more. The two together are still narrower than a square corner. Still acute. Two half-of-a-quarter turns. 1/8 turn + 1/8 turn = 2/8 turn = 1/4 turn. That is exactly a square corner. A right angle, not acute. Two big acute turns. Turn nearly a quarter, then nearly a quarter again. Together they are wider than a square corner. Obtuse. 1/8 + 1/8 = 2/8 = 1/4 turn → right angle 1/12 + 1/12 = 2/12 = 1/6 turn → still acute 1/6 + 1/6 = 2/6 = 1/3 turn → obtuse start end 1/12 turn and another 1/12 turn together make a 1/6 turn — still acute. Why it happens: An angle is acute only while it stays less than a quarter turn . Two acute turns can add up to less than a quarter turn, exactly a quarter turn, or more than a quarter turn — so all three answers are possible. The rule is about the total, not about the two pieces. Sample answer: “Yes, two acute turns can make another acute turn, but only if they add up to less than a quarter turn. If they add up to more, the angle becomes obtuse.”

NCERT Solutions for Class 5th Maths Chapter 3 Adding two turns — In-text Questions