Find out the number of acute angles in each of the figures below. What will be the next figure and how many acute angles will it have?

Find out the number of acute angles in each of the figures below. What will be the next figure and how many acute angles will it have? Class 6

Question 1.

Find out the number of acute angles in each of the figures below. Class 6

What will be the next figure and how many acute angles will it have? Do you notice any pattern in the numbers?

Solution:

In the first figure, the number of acute angles is 3.

In the second figure, the number of acute angles is 12.

And in the third figure, the number of acute angles is 21.

The next figure may be

The number of acute angles in this figure is 30.

Thus, the pattern in these numbers is 3, 12, 21, 30, ...

i.e., 3 × 1, 3 × (1 + 3), 3 × (1 + 2 × 3), 3 × (1 + 3 × 3), ...

In other words, it is 3 × 1, 3 × 4, 3 × 7, 3 × 10, 3 × 13.

Some students may draw the next figure as shown below:

Here also, the number of acute angles is 30.

Thus, in this case, the next figure may be drawn in some other ways, and it is possible that the answer may not be unique.