Question

What type of angles are labeled and what is the value of x? Show your work.

Answer 1

2x-30 is an acute angle

x+60 is an obtuse angle

x=50

Explanation:

So the all the angle on a straight line add up to 180 degrees

So we can make an equation

`2x - 30 + x + 60 = 180`

Then we move like terms on either side of the equation and remember when we move them to the other side the sign changes.

`2x + x = 180 + 30 - 60`

then we simplify both sides

`3x = 150`

to get X on its own we must divide both sides by three

`(3x)/(3) = (150)/(3 \\ ) \\ x = 50`

Answer 2

Angles on a straight line are supplementary. Solving x + 60 = 120 and
2x + 30 = 60 gives x = 60. Thus, the angles are supplementary, verifying the result.

On a straight line, angles are called supplementary because their sum is 180 degrees. Given angles x + 60 = 120 and 2x + 30 = 60, let's solve for x.

1. Equation 1: x + 60 = 120

- Subtract 60 from both sides: x = 60

2. Equation 2: 2x + 30 = 60

- Subtract 30 from both sides: 2x = 30

- Divide by 2: x = 15

Now, we verify the sum of the angles on the straight line:

x + (2x + 30) = 60 + 120 = 180

Therefore, angles labeled on a straight line are supplementary. \(x\) is 60, and the angles are consistent with this property, confirming the solution's accuracy.