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.

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=\frac{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)

$m\angle1=106\degree$