100 POINTS! PLEASE HELP! 1. What is the value of x? Enter your answer in the box. x = __

2. What is the value of x? Enter your answer in the box. x = __

(images below)

1. x=5. 2. x=3

Step-by-step explanation:

Ok, so I actually spent 2 hours doing the first problem, I considered the angles to be different at first, i will add my messy work if you are interested haha.

However, I realized that the only way this question can be possible to solve is if the angles are equal, and there is no information given to say that they are different (they are both indicated by one line, while angles that are different are usually represented with multiple lines).

The general method for such problems is to consider the ratio of the sides to the side lengths into which the long side is divided.

For the first picture, the answer can be found by: 9/(2x-1) = 15/(3x). From here, we find that x = 5 (do some algebra). I actually got the same answer when doing this problem with the sine rule.

I am only looking now at the second problem, and i can tell straight away that we can get the solution by solving 3/2.25 = 4/x. x = 3 after some algebraic manipulation.

So yeah, this was a not so fun experience of trying to do this problem without knowing the angles were equal, but i learned a lot haha :)

PS. I am only adding my terrible working out because i hate myself for being so silly

why can't you?

step-by-step explanation:

∠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.