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satela [25.4K]
3 years ago
9

Please help me is for my homework​

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
7 0

I hope this help you

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Given: mAngleEDF = 120°; mAngleADB = (3x)°; mAngleBDC = (2x)° Prove: x = 24 3 lines are shown. A line with points E, D, C inters
N76 [4]

Answer:

" Vertical angles are congruent " ⇒ 2nd answer

Step-by-step explanation:

* <em>Look to the attached figure </em>

- There are three lines intersected at point D

- We need to find the missing in step 3

∵ Line FA intersects line EC at point D

- The angles formed when two lines cross each other are called

 vertical angles

- Vertical angles are congruent (vertical angles theorem)

∴ ∠ADC and ∠FDE are vertical angles

∵ Vertical angles are congruent

∴ ∠EDF ≅ ∠ADC

∴ m∠EDF ≅ m∠ADC

∵ m∠EDF = 120° ⇒ given

∵ m∠ADC = m∠ADB + m∠BDC

∴ m∠ADB + m∠BDC = 120°

∵ m∠ADB = (3x)° ⇒ given

∵ m∠BDC = (2x)° ⇒ given

∴ 3x + 2x = 120 ⇒ add like terms

∴ 5x = 120 ⇒ divide both sides by 5

∴ x = 24

Column (1)                                                     Column (2)

m∠EDF = 120°                                               given

m∠ADB = 3 x                                                 given

m∠BDC = 2 x                                                 given

∠EDF and ∠ADC are vertical angles           defin. of vert. ∠s

∠EDF is congruent to ∠ADC                        vertical angles are      

                                                                        congruent  

m∠ADC = m∠ADB + m∠BDC                        angle add. post.

m∠EDF = m∠ADC                                          defin. of cong.

m∠EDF = m∠ADB + m∠BDC                         substitution

120° = 3 x + 2 x                                               substitution

120 = 5 x                                                         addition

x = 24                                                              division  

∴ The missing reason is " vertical angles are congruent "

- From the explanation above ∠ADC and ∠FDE are vertical

 angles then they are congruent according to vertical angle

 theorem

6 0
3 years ago
Read 2 more answers
The Larger of two numbers is 27 more than the smaller. When added together , the sum of the larger number and five times the sma
Genrish500 [490]

Answer:

Small no. is 15

Larger no. is 15 + 27 = 42

Step-by-step explanation:

Let the small no. be x

Larger no. will be x + 27

5x + x + 27 = 117

6x + 27 = 117

6x = 117-27

x = 90/6

x = 15

4 0
3 years ago
It takes 2 1/3 hours to paint a wall. How long will it take to paint 7 walls at this rate?
boyakko [2]

Answer:

Hi! The correct answer is 49/2 as an improper fraction and 24 1/2 in mixed number form!

Step-by-step explanation:

<em><u>~If it takes 2 and 1/3 to paint 1 wall then that's the unit rate. Multiply the unit rate by the number of total walls and that's your answer~</u></em>

7 0
3 years ago
Draw a graph of Lin's distance of a function of time for this situation:
Pavlova-9 [17]

Step-by-step explanation:

Given

Lin walks half a mile at a constant rate i.e. Lin velocity is constant. So, in the graph, it will be a straight line through the origin.

Lin is still for five minutes and after she began sprinting for the slip up to halfway i.e. Lin is accelerating or velocity is increasing for the halfway and later she started walking for the rest of the way.

3 0
2 years ago
Find the maximum value of the function f(x) = -1.9x^2 + 24x – 71.3 to the<br> nearest hundredth.
d1i1m1o1n [39]
Being that the system is quadratic—with parabola opening downwards—you’re going to need to find the vertex. You can find the x coordinate of the vertex with -b/2a . Then plug in for x to find the y coordinate…
4 0
2 years ago
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