Question

Analyze the diagram below and complete the instructions that follow. Find the value of x.
A)9
B)18
C)45
D)90

Answer 1

Answer:

The value of x is: $x=18$. Therefore, correct answer is option (B).

Step-by-step explanation:

We can see that the angles $4x$ and $(2y-x)$ are vertical angles, therefore, we can set them equal to each other to get an equation as shown below:

$4x=2y-x$

Furthermore, we can see that angles $(2y+x)$ and $(2y-x)$ are linear pair angles, therefore, we can set up another equation as shown below:

$(2y+x)+(2y-x)=180$

$2y+x+2y-x=180$

$4y=180$

$y=45$

Upon substituting this value in the first equation, we get:

$4x=2(45)-x$

$4x=90-x$

$5x=90$

$x=18$

Therefore, the value of x is 18 degrees and thus, the correct answer is option (B).

Answer 2

The value of x is ${18^ \circ }$. Option (b) is correct.

Further Explanation:

Vertical angles can be defined as the angles that are opposite to each other if two lines cross each other.

Acute angles are those angles in which the measurement of the angle is less than ${90^ \circ }.$

Given:

The options are as follows,

(a). 9

(b). 18

(c). 45

(d). 90

Explanation:

Angle ${\left( {4x} \right)^ \circ }$ and angle ${\left( {2y - x} \right)^ \circ }$ are vertical opposite angle and the vertical opposite angles are equal.

$\begin{aligned}4x&=2y - x\\5x&= 2y\\\frac{5}{2}x&= y\\\end{aligned}$

Angle ${\left( {4x} \right)^ \circ }$ and angle ${\left( {2y + x} \right)^ \circ }$ are linear pair. Therefore, the sum of the angles is ${\left( {2y + x} \right)^ \circ }$

$\begin{aligned}4x + 2y + x &= 180\\5x + 2y&= 180\\5x + 2\times\frac{5}{2}x&= 180\\\end{aligned}$

Further solve the above equation to obtain the value of x.

$\begin{aligned}5x + 5x&= 180\\10x&=180\\x&=\frac{{180}}{{10}}\\x&= 18\\\end{aligned}$

Hence, the value of x is ${18^ \circ }.$

Option (a) is not correct as value of x is not 9.

Option (b) is correct as the value of x is 18.

Option (c) is not correct as value of x is not 45.

Option (d) is not correct as value of x is not 90.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Angles

Keywords: vertical angle, opposite angle, angles, alternate angles, linear pair, corresponding angles, analyze, value of x.