Two parallel lines are crossed by a transversal. What is the value of k? k = 9 k = 20 k = 60 k = 71
1 answer:
your question seems missing the figure.
I am attaching the required figure below.
You can study the correct answer to your question and complete explanation with the figure below.
Answer:
k=60
Step-by-step explanation:
When a pair of parallel lines is crossed by a transversal, it will make 8 angles, pairs of vertical/opposite angles, two pairs of acute angles and two pairs of obtuse angles. All acute angles are congruent as well as all obtuse angles are congruent. Simply we can say that pairs of acute angles and pairs of obtuse angles are congruent.
From the figure attached below (by the name "Pairs of parallel lines crossed by a transversal"), we get the following equations as:
2k+11=131
Solving for k, we get
2k=131-11
2k=120
k=120/2
k=60
You might be interested in
First, let us break down 28 hours 36 minutes into minutes.
Number of minutes taken to grade 220 essays = (28 x 60) + 36 = 1680 + 36 = 1716 minutes
Now, we can find the average time taken to grade an essay by dividing the time taken to grade 220 essays by 220.
Average amount of time taken to grade an essay = = 7.8 minutes, or 7 minutes and 48 seconds
The solution to these equations is (x, y) = (2, 4).
We've not heard of a method of solving a linear system using the x- and y-intercepts. A Google search on the subject turns up this question, and no other information. However, there is information you can gain from the intercepts that can help you find a solution. (Your reference material may provide a better source of information on this subject.)
The <em>intercept form</em> of a linear equation is ...
... x/(x-intercept) + y/(y-intercept) = 1
Dividing the first equation by 4, you can rearrange it to ...
... x/(-2) +y/(2) = 1 . . . . . . the x-intercept is -2, the y-intercept is +2.
Dividing the second equation by -6, you can rearrange it to ...
... x/-6 +y/3 = 1 . . . . . . . . the x-intercept is -6, the y-intercept is +3.
_____
<em>What you can do with the intercepts</em>
The intercepts can be used to <em>graph the equations</em>. Plot each of the intercepts for a given equation, then draw a line through them. (See the attachment.)
Here, both lines have their intercepts on the negative x and positive y axes. The slopes and intercepts of the lines are such that they intersect in the 1st quadrant.
We can use the intercepts to <em>find the slope of the line</em>.
The slope of each line can be found from ...
... slope = -(y-intercept)/(x-intercept)
Then the slope of the first line is ...
... m1 = -2/-2 = 1
and the slope of the second line is ...
... m2 = -3/-6 = 1/2
The difference in slopes is ...
... m1 - m2 = 1 - 1/2 = 1/2
Using the slope and intercept we can <em>find the solution</em> by substitution or elimination.
For line 1 with slope m1 and y-intercept b1, the equation of the line in slope-intercept form is
... y = m1·x + b1 = x +2
For line 2 with slope m2 and y-intercept b2, the equation of the line in slope-intercept form is
... y = m2·x +b2 = (1/2)x +3
Subtracting the second equation from the first eliminates the y-variable and gives ...
... y - y = 0 = (x +2) -(1/2x +3) = 1/2x - 1
Adding 1 and multiplying by 2 gives the solution for x:
... x = 2
Then the first equation gives the solution for y:
... y = x + 2 = 2+2 = 4
The solution is (x, y) = (2, 4).
_____
<em>Comment on </em><em>find the solution</em>
Above, we subtracted one equation from the other to get ...
... y - y = 0 = x(m1 -m2) +(b1 -b2)
We could have simply equated the values of y to get ...
... m1·x +b1 = y = m2·x +b2
Either way you do this, you find the solution for x is ...
... x = (b2 -b1)/(m1 -m2)
- Calculate
- Divide both sides by 4296875
- Answer