Question

Given m∥n, find the value of x and y.

Answer 1

x = 15

y = 63

Explanation:

9x - 7 + 4x - 8 = 180

13x = 195

x = 15

9x - 7 = 2y + 2

126 = 2y

y = 63

Answer 2

The correct answer is:

x = 15

y = 63

Defining Key Terms

To begin, an understanding of the types of angles must be established.

• Alternate Interior Angles: Alternate interior angles are angles that oppose one another and are interior (not on the outside of the transversal/figure). An example is supplied in the image. In this instance, the angle measurements (9x - 7)° and (2y + 2)° are alternate interior angles.

• Supplementary Angles: Supplementary angles are situated on the same straight line, on the same side of the straight line, and add up to 180° measurements. In this instance, the angle measurements (4x - 8)° and (9x - 7)° are supplementary angles.

Solve - Supplementary Angles (x-term)

An equation can be devised since both angle measurements will equal 180°. It can be said that:

`x+y=180`

Assigning a variable to an angle measurement (the assignment does not matter in this scenario):

`x: (4x - 8)^(\circ) \\y: (9x-7)^(\circ)`

Then, substitute the new values into the devised equation:

`(4x-8)+(9x-7)=180`

Then, drop the parentheses and combine like terms:

`4x-8+9x-7=180\\\\\text{Add 4x and 9x to combine like terms:} \ 13x-8+-7=180\\\\\text{Add -8 and -7 to combine like terms:} \ 13x-15=180`

Then, add 15 to both sides of the equation to isolate the term hosting the variable:

`13x-15+15=180+15\\\\13x=195`

Finally, divide by 13 on both sides to isolate the variable:

`\displaystyle (13x)/(13)=(195)/(13)\\\\\boxed{x=15}`

Therefore, x = 15.

Then, substitute the x-value into the angle measurement (9x - 7) to solve for the angle measurement in degrees:

`9(15)-7\\\\135-7\\\\\bold{128}^\circ`

Solve - Alternate Interior Angles (y-term)

Then, using the new measurement for the angle alternate to (2y + 2)°, since alternate interior angles are congruent (equal), an equation can be devised that sets the unknown angle equal to the known angle:

`(2y+2)=128`

Then, subtract 2 from both sides to isolate the term hosting the variable:

`2y+2-2=128-2\\\\2y=126`

Finally, divide both sides by 2 to isolate the variable:

`\displaystyle (2y)/(2)=(126)/(2)\\\\\boxed{y=63}`

Therefore, y = 63.

Final Answer

Therefore, x = 15 and y = 63.