Question

In the diagram below, line / and m are parallel lines. Also, line p and q areparallel lines.Given:• m22=(x) °m23-106⁰m2 4=(2y)•1.2.3.#mWhat is the value of x?What is the value of y?What is the value of z and measure of angle 1?I

Answer 1

Given:

line l and m are parallel lines.

line p and q are parallel lines.

`m\angle2=(x)\degree,m\angle3=106\degree,\text{ and }m\angle4=(2y)\degree`

Required:

We need to find the value of x and y and measure of angle 1.

Step-by-step explanation:

`C\text{orresponding angles }\angle2\text{ and }\angle3\text{ are congruent since l and m are parallel.}`
`m\angle2=m\angle3`
`Substitute\text{ }m\angle2=(x)\degree\text{and }m\angle3=106\degree in\text{ the equation.}`
`(x)\degree=106\degree`
`x=106`

The sum of the supplementary angles is 180 degrees.

`\angle4\text{ and }\angle3\text{ are supplementary angles.}`
`m\angle4+m\angle3=180\degree`
`Substitute\text{ }m\angle3=106\degree\text{ and }m\angle4=(2y)\degree\text{ in the equation.}`
`(2y)\degree+106\degree=180\degree`
`(2y)\degree=180\degree-106\degree`
`(2y)\degree=74\degree`
`y=(74)/(2)`
`y=37`

`C\text{orresponding angles }\angle1\text{ and }\angle2\text{ are congruent since p and q are parallel.}`
`m\angle1=m\angle2`
`Substitute\text{ }m\angle2=106\degree\text{ in the equation.}`
`m\angle1=106\degree`

Final answer:

1)

`x=106`

2)

`y=37`

3)

`m\angle1=106\degree`