Given that we assume that all the bases of the triangles are parallel.
We can use AAA or Angle-Angle-Angle to prove that these triangles are similar.
Each parallel line creates the same angle when intersecting with the same side.
For example:
The bases of each triangle cross the left side of all the triangle.
Each angle made by the intersecting of the the parallel base and the side are the same.
Thus, each corresponding angle of all the triangles are congruent.
If these angles are congruent, then we have similar triangles.
Answer:
x ≈ 36.9°
Step-by-step explanation:
Using the sine ratio in the right triangle, that is
sinx = 
= 
, then
x = 
( ) ≈ 36.9° ( to 1 dec. place )
Answer: I got answers A, B and E
Step-by-step explanation:
Well first you have to make variables for each number.
1st - x
2nd - y
3rd - z
first sentence says twice first number so 2x. is means equals so =. eleven more than sum of the other two numbers. sum of other two numbers is (y + z) and eleven more than that is (y + z) + 11. So so this sentence says:
2x = (y + z) + 11
second sentence says sum of twice the first and three times third. twice first is 2x and three times third is 3z. their sum would be (2x + 3z). It it says is one more than second number. So = (y + 1). So so this means:
(2x + 3z) = (y + 1)
third sentence says second number (y) is is equal to sum of first and third (x + z). so;
y = (x + z)
now for the work.
We we can easily solve for a by subtracting the first 2 equations. the way to subtract 2 equations is by subtracting one left side of equal sign from the other equations left side and then doing the same with the right side.
So we will subtract the 1st and second equations we made.
So so left sides would be
2x - (2x + 3z)
2x - 2x - 3z
-3z
right side would be:
y + z + 11 - (y + 1)
y + z + 11 - y - 1
z + 10
now put the sides with an equal sign
-3z = z + 10
-4z = 10
z = -2.5
now we can plug in z into the equations and subtract second and third equations. But but we will subtract opposite sides. So so left minus right and right mi is left after we plug in z:
(2x + 3 (-2.5)) - (x + (-2.5))
2x - 7.5 - x + 2.5
x - 5
other one would be
(y + 1) - y
1
So so put an equal sign and get:
x - 5 = 1
x = 6
now plug x and x into 3rd equation
y = x + z
y = 6 + (-2.5)
y = 3.5
now we have values. You can check answer by plugging values into other 2 equations
