How many triangles would be in the 57th figure?

Figure One:

3 triangles

Figure two:

5 triangles

FIgure three:

7 triangles

115

Step-by-step explanation:

Consider the sequence of triangles

3, 5, 7

There is a common difference between consecutive terms, that is

d = 7 - 5 = 5 - 3 = 2

This indicates the sequence is arithmetic with n th term

= a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 3 and d = 2, thus

= 3 + (56 × 2) = 3 + 112 = 115

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.

answer: the anser is 3

step-by-step explanation:

c- 2o is equal to 9