Given A is between Y and Z and YA = 2x, AZ = 16x, and YZ = 4x+56, find AZ.<br> Plsss help

yawa3891 [41]

Answer:

$1)\ x = 5$

$2)\ x = 14$

$3) \ x = 15,\ y = 2$

Step-by-step explanation:

1) Given that M<1 = 95 + 7x and M<2 = 55 - x, you should look on the diagram to see what type of angles M<1 and M<2 are.

On the diagram at the top, angles 1 and 2 appear to be supplementary angles, meaning they add up to 180 degrees. You can apply this information to creating an equation:

M<1 + M<2 = 180°

$(95 + 7x) + (55 - x) = 180$

Now you can solve this equation by combining like terms on the left-hand side of the equation.

$150+6x=180$

Subtract 150 from both sides of the equation in order to isolate the variable x.

$6x=30$

Divide both sides of the equation by 6 in order to isolate the variable x completely.

$x=5$

2) You are given that M<3 = 5x + 12 and M<4 = 7x - 16, so look on the diagram at the top to find out what type of angles they are.

Angles 3 and 4 appear to be alternate exterior angles, meaning that they are equal to each other as stated by the Alternate Exterior Angles Theorem. You can use this information to make an equation where M<3 = M<4.

M<3 = M<4

$5x+12=7x-16$

Subtract 5x from both sides of the equation, and add 16 to both sides of the equation.

$28=2x$

Divide both sides of the equation by 2 to isolate the variable x completely.

$14=x \rightarrow x=14$

3) Given that M<1 = 7y + 16, M<2 = 2x, and M<3 = 4x - 30, look on the diagram at the bottom to find out what type of angles they are.

Since angles 2 and 3 include an "x" variable, you should start with them first in order to be able to solve for x. Angles 2 and 3 are complementary angles, meaning that they are equal to each other based on the Complementary Angles Theorem. Translate this information into an equation:

M<2 = M<3

$2x=4x-30$

Subtract 2x from both sides of the equation and add 30 to both sides of the equation.

$30=2x$

Divide both sides of the equation by 2 in order to isolate the variable x completely.

$15=x \rightarrow x=15$

Now to solve for y - based on the diagram, you can see that angle 1 and angle 2 are vertical angles, meaning that they are equal to each other based on the Vertical Angles Theorem.

You can make them equal to each other in an equation: