Question

Find the value of x and y and each labeled
angle.

Answer 1

x = 40

3x - 20 = 100

2x = 80

y = 80

2x - 15 = 65

Explanation:

The angles 3x - 20 and 2x are a linear pair, so they are supplementary. Their measures has a sum of 180°.

Angles 2x and y are alternate interior angles, so they are congruent.

Once we find the value of x, we can find the measure of angle 2x - 15.

3x - 20 + 2x = 180

5x = 200

x = 40

3x - 20 = 3(40) - 20 = 120 - 20 = 100

2x = 2(40) = 80

y = x = 80

2x - 15 = 2(40) - 15 = 80 - 15 = 65

Answer 2

`▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪`

The required values are ~

`\fbox \colorbox{black}{ \colorbox{white}{x} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{40 \degree}}`

`\fbox \colorbox{black}{ \colorbox{white}{y} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{80 \degree}}`

`\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}`

From the given figure, we can infer that ~

• 3x - 20° + 2x = 180°

(by linear pair)

now, let's solve for x ~

• 
  `5x - 20 \degree = 180 \degree`

• 
  `5x = 180 \degree + 20 \degree`

• 
  `5x = 200 \degree`

• 
  `x = 200 \degree / 5`

• 
  `x = 40 \degree`

And, we can see that 2x = y (by alternate interior angle pair)

So, let's find the value of y ~

• 
  `2x`

• 
  `2 * 40 \degree`

• 
  `80 \degree`