Question

NO LINKS! Please help me with this problem​

Answer 1

x = 70°

y = 55°

Explanation:

The angle sum theorem and the definition of a linear pair can be used to write two equations in the two unknowns. Those can be solved for the angle values.

Setup

x + y + y = 180° . . . . . . angle sum theorem

y + (2x -15) = 180° . . . . definition of linear pair

Solution

We can use the first equation to write an expression for x that can be substituted into the second equation:

x = 180 -2y

y +(2(180 -2y) -15) = 180 . . . . substitute for x

345 -3y = 180 . . . . . . . . . . . collect terms

115 -y = 60 . . . . . . . . . . . . .divide by 3

y = 55 . . . . . . . . . . . . . . add (y-60)

x = 180 -2(55) = 70

The values of the variables are ...

x = 70°

y = 55°

exterior angle = 125°

Answer 2

x=70, y=55

Explanation:

Since the angle "y" and 2x-15 form a straight line, that means the sum of the angles, must be 180 degrees.

So using this we can derive the equation:
`y+2x-15=180`

The next thing you need to know is that the sum of interior angles of a triangle is 180 degrees, so if we add all the angles, we should get 180.

So using these we can derive the equation:
`x+2y=180`

So, in this case we simply have a systems of equations. We can solve this by solving for x in the second equation (sum of interior angles), and plug that into the first equation.

Original Equation:

`x+2y = 180`

Subtract 2y from both sides

`x = 180-2y`

Now let's plug this into the first equation

`y+2x-15=180`

Plug in 180-2y as x

`y+2(180-2y)-15=180`

Distribute the 2

`y+360-4y-15=180`

Combine like terms

`-3y + 345 = 180`

Subtract 345 from both sides

`-3y = -165`

Divide both sides by -3

`y=55`

So we can plug this into either equation to solve for x

`x+2y=180`

Substitute in 55 as y

`x+2(55)=180`

`x+110=180`

Subtract 110 from both sides

`x=70`