1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
olchik [2.2K]
2 years ago
8

Question included in the image - geometry problem.

Mathematics
1 answer:
iren [92.7K]2 years ago
5 0

Answer:

y = 116°

Step-by-step explanation:

Given that <em>L₁ </em>|| <em>L</em>₂:

The <u>exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the two opposite and non-adjacent remote interior angles.  

Also, ∠y° and ∠2x° are <u>same-side interior angles</u> formed by the intersection of the <em>hypotenuse</em> of the triangle that acts as a transversal to the parallel lines, <em>L₁ </em>and <em>L</em>₂.  Given that ∠y° and ∠2x° are <u>same-side interior angles</u>, then it means that they are the supplements of each other, such that the sum of their measures is 180°.  

Now that we have established these definitions, we can proceed with the solution.

<u>Equation 1</u>:  ∠y° + ∠2x° = 180° ⇒ Same-side interior angles

<u>Equation 2</u>:  ∠y° =  ∠x° + ∠84°  ⇒ exterior angle theorem

Substitute the value of m∠y° from Equation 2 into Equation 1 to solve for the value of x:

∠y° + ∠2x° = 180°

∠x° +  ∠84° + 2x° = 180°

Combine like terms:

∠3x° + ∠84° = 180°

Subtract ∠84° from both sides:

∠3x° + ∠84° - ∠84° = 180° -∠84°

∠3x° = 180° - ∠84°

∠3x° = 96°

Divide both sides by 3 to solve for x:

\frac{3x}{3} = \frac{96}{3}

∠x° = 32°

Substitute the value of x into Equation 2 to solve for y:

∠y° =  ∠x° + ∠84°

∠y° =  ∠32° + ∠84°

∠y° =  116°

Verify whether the values for x and y are correct by substituting their values into Equation 1 and 2:

<h3>Equation 1:</h3>

∠y° + ∠2x° = 180°

116° + 2(32)° = 180°

116° + 64° = 180°

180° = 180° (True statement).

<h3>Equation 2:</h3>

∠y° =  ∠x° + ∠84°

116° = 32° + 84°

116°  = 116°  (True statement)

Therefore, the correct answer is: y = 116°.

You might be interested in
Which of the lines below is parallel to a line with a slope of 3 and a y-intercept at (0, 3)?
Dmitrij [34]

Answer:

\displaystyle line\:HJ

Step-by-step explanation:

\displaystyle y = 3x + 3

The descryption gives you the above <em>Slope-Intercept Equation</em>. Parallel equations have SIMILAR <em>RATE</em><em> </em><em>OF</em><em> </em><em>CHANGES</em><em> </em>[<em>SLOPES</em>], therefore \displaystyle 3 remains as is, and perfourming \displaystyle \frac{rise}{run}, will give you that answer.

I am joyous to assist you at any time.

6 0
2 years ago
Tyrone mixed 7/12 quart of red psont with 1/12 quart of yellow paint how much paint does tyrone have in the mixture
Zarrin [17]
Hello there.

<span>Tyrone mixed 7/12 quart of red paint with 1/12 quart of yellow paint how much paint does Tyrone have in the mixture?
</span><span>
Answer: In this question you need to add together the fractions provided.
The sum would look like this:
</span>\frac{7}{12} + \frac{1}{12} =
<span>Since the denominators are the same , it is simple to add.
All you need to do is 7 + 1 = 8.
Therefore the end result after solving would look like.
</span>\frac{7}{12} + \frac{1}{12} = \frac{8}{12}.
<span>Tyrone has 8/12 quarts of paint.

Hope This Helps You!
Good Luck Studying ^-^</span>
3 0
3 years ago
When steve woke up. his temerature was 102. two hours later it was 3 lower what is his temerature now?
valentina_108 [34]
Steve's original temperature - 102

2 hours later it dropped 3 degrees

102 - 3 = 99

Steve's current temperature is 99.
8 0
3 years ago
Ind the slope and y intercept of -9x+3y=5
Radda [10]

Answer:

first, you need to get y on one side. So, because the x is negative it becomes positive when you switch it to the other side. 3y= 9x+5. You then need to divide all parts by 3. 3/3= 1 so thats just y. 9/3 is 3 so thats 3x. then 5/3 is a fraction that you can write as just 5/3 or 1 and 2/3. That would leave you with y= 3x + 5/3. Then x (3) is your slope. and what you add to it (5/3) is your y int.

4 0
2 years ago
In a city the record monthly high temperature for july is 88. The record monthly low temperature is 30.
Zinaida [17]

Answer:

 58 degrees    or   [30, 88]

Step-by-step explanation:

In such a context, the word "range" can have different meanings. On the one hand it is the difference between high and low:

  88 -30 = 58 . . . . range of temperatures

__

On the other hand, it is the interval between (and including) the high and low:

  [30, 88] . . . . temperature range

3 0
3 years ago
Other questions:
  • Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −4 is the only other
    14·1 answer
  • The sum of three numbers is 7. One of the numbers is one more than the sum of the other two numbers. It is also four times the d
    8·2 answers
  • When the buyer for superior electronics took physical inventory of the blue ray players on July 31, 66 units remained in invento
    6·1 answer
  • Common letter-sized paper used in the united states has what dimensions? 8.27" x 11.69" 8.5" x 14" 8.5" x 11" 8" x 11.5"
    15·1 answer
  • A college graduating class consists of 450 students. There are 206 more females than males. Determine the number of male and fem
    13·2 answers
  • PLEASE HURRY Quadilateral abcd is inscribed in circle z such that AB is parallel to DC and m
    7·1 answer
  • What is the area for this?
    12·2 answers
  • Maria had 10.5 pounds of flour. She used all of the flour to fill bags that hold 0.75 pound each.
    9·2 answers
  • Use the figure shown below to find the value of x
    13·1 answer
  • Tom has saved $390. He plans to spend $30 each month for music lessons. The function
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!