NEED THIS PLS HELP!!!!!!

Mathematics

2 answers:

erastovalidia [21]2 years ago

8 0

Answer:

x = 7 , y = 37

Step-by-step explanation:

For Δ LMN ≅ Δ PQR

Then corresponding angles must be congruent, that is

∠ P = ∠ L , substitute values

9x - 18 = 5x + 10 ( subtract 5x from both sides )

4x - 18 = 10 ( add 18 to both sides )

4x = 28 ( divide both sides by 4 )

x = 7

Then

∠ P = 9x - 18 = 9(7) - 18 = 63 - 18 = 45°

∠ R = 180° - (84 + 45)° ← sum of angles in a triangle = 180°

∠ R = 180° - 129° = 51°

Then ∠ N = ∠ R

2x + y = 51

2(7) + y = 51

14 + y = 51 ( subtract 14 from both sides )

y = 37

RoseWind [281]2 years ago

6 0

Answer:

$x=7$

$y=37$

Step-by-step explanation:

So if the angle of $Q=M$ we can assume that $P=L$ and $N=R$ . Since we don't have the equation for $R$ let's start with $P$ and $L$ .

If $P=L$ that means that $(5x+10)=(9x-18)$ from there we can subtract $5x$ which makes it so that $(10)=(4x-18)$ from there we can add 18 to each side so we have $28=4x$ from there we simply divide both sides by 4 which gives us $x=7$ ° we can then check that this is correct by doing $5*7+10$ which gives us 45° for $L$ and then $9*7-18$ which gives us 45° for $P$

Since we know that the sum of the interior angles of all triangles has to be 180° that means that we can figure out the angle of $N$ and $R$ by doing $180-(84+45)$ which is 51. Assuming that $N=51$ ° we can write something like $(2)(7)+y=51$ which can be simplified into $14+y=51$ , then you remove the 14 by subtracting it from both sides which leaves $y=37$ . Once again we have to double-check so $(2)(7)+37=N$ and $2*7=14$ so $14+37$ obviously equals 51.