Question

An ant leaves the anthill for its morning exercise. Its walks 4 feet east and then
makes a 160° turn to the right and walks 4 more feet. It then makes another 160° turn to the right and walks 4 more feet. If the ant continues this pattern until it reaches the anthill again, what is
the distance in feet it would have walked?(PRMO-2019)​

Answer 1

Answer:

72

Step-by-step explanation: it takes 160°turn to the write hence turns 20° left and 360/20= 18 therefore a it will make a regular polygon of 18 sides to reach the initial point and 18×4= 72

Answer 2

Answer:

Total distance travelled = 72 feet

Step-by-step explanation:

In the question,

Firstly the ant walks for 4 feet in East direction and then takes a 160° turn right and walks 4 feet again.

So, for the ant to reach the initial position from where it started it will have to complete a 360° revolution because,

For every turn it is left of the 20° as,

180° - 160° = 20°

So,

For the ant to reach the initial position of the anthill.

He will have to take 360° cover.

So,

Number of turns, n = $\frac{360}{20}=18$ turns

Therefore, it has to turn 18 times.

So,

Total distance travelled by the ant = Number of turns x Distance travelled in 1 turn

Total distance travelled = 18 x 4 = 72 feet