Given: Lines y and z are parallel, and ABC forms a triangle. Prove: m∠5 + m∠2 + m∠6 = 180° Lines y and z are parallel. Triangle A B C sits between the 2 lines with point A on line y and points C and B on line z. Angle C A B is 2. Its exterior angle to the left is 1 and its exterior angle to the right is 3. Angle A B C is 6 and its exterior angle to the right is 7. Angle B C A is 5 and its exterior angle to the left is 4. Statements Reasons 1. ABC is a triangle 1. given 2. y ∥ z 2. given 3. ∠1 ≅ ∠5; ∠3 ≅ ∠6 3. ? 4. m∠1 = m∠5; m∠3 = m∠6 4. def. ≅ 5. m∠1 + m∠2 + m∠3 = m∠LAM 5. ∠ addition postulate 6. m∠1 + m∠2 + m∠3 = 180° 6. def. Straight angle 7. m∠5 + m∠2 + m∠6 = 180° 7. substitution Which could be the missing reason in Step 3? alternate interior angles are congruent alternate exterior angles are congruent vertical angles are congruent corresponding angles are congruent

Answers

Answer 1

Answer:

The correct option is;

Alternate interior angles

Step-by-step explanation:

The m∠5 + m∠2 + m∠6 = 180° proof is given as follows;

Statement                [tex]{}[/tex]                        Reason

1. ABC is a triangle              [tex]{}[/tex]             Given

2. y ║ z                                [tex]{}[/tex]              Given

3. ∠1 ≅ ∠5; ∠3 ≅ ∠6                         Alternate interior angles

4. m∠1 = m∠5; m∠3 = m∠6        [tex]{}[/tex]       Definition of (congruency) ≅

5. m∠1 + m∠2 + ∠3 = m∠LAM        [tex]{}[/tex]  ∠Addition postulate

6. m∠1 + m∠2 + ∠3 = 180°        [tex]{}[/tex]        Definition of straight angles

7. m∠5 + m∠2 + ∠6 = 180°        [tex]{}[/tex]        Substitution property

Step 3;

Given that line y is parallel to line z, we have that the transversal AB will make equal corresponding angles with the lines y and z, therefore, ∠6 will be equivalent to segment AB extended

Which gives, ∠6 is supplementary to ∠a where ∠a = ∠1 + ∠2

Therefore, given that ∠3 is also supplementary to ∠a where as we have above, ∠a = ∠1 + ∠2, we have that ∠3 = ∠6 and ∠3 ≅ ∠6 where ∠3 and ∠6 are alternate interior angles;

Similarly, ∠1 ≅ ∠5 by alternate interior angles of two parallel lines property.

Given: Lines Y And Z Are Parallel, And ABC Forms A Triangle. Prove: M5 + M2 + M6 = 180 Lines Y And Z
Answer 2

Answer:

The answer is A. alternate interior angles are congruent

Step-by-step explanation:

I tried all my options and that one was correct.


Related Questions

Write an algebraic expression for the statement.
The cost of m pounds of meat when the cost per pound is $3.54.

Answers

Answer:

y=3.54m

Step-by-step explanation:

it is pretty self explanatory

An algebraic expression for the statement could be as; y = 3.54m

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

Thus which can also be used to indicate the logical syntax's order of operations and other features.

We need to write an algebraic expression for the statement.

Given that The cost of m pounds of meat when the cost per pound is $3.54.

Therefore, the expression could be as;

y = 3.54m

hence, An algebraic expression for the statement could be as; y = 3.54m

To know more about an expression follow;

brainly.com/question/19876186

#SPJ2

Seven times the difference of triple a number and three

Answers

Answer:

21x- 21

Step-by-step explanation:

7 × (x × 3 - 3)

7 × (3x - 3)

21x - 21

I'm not sure if the answer is correct

Pls answer and show WORK pls do it right

Answers

Answer:

4/6

Step-by-step explanation:

1/2 needs to be converted to sixths, so we would multiple the numerator and the denominator by 3, because 2 goes into 6, 3 times, then we would get 3/6 + 1/6, then just add, 1 + 3 = 4, and then you end up with 4/6. Have A Great Day!

Twelve Divided by the sum of a number and five

Answers

12/x+5
x represents “a number” because it’s unknown and the + sign is because the words sum

Expand & simplify 4(t+2)+6(t-4)

Answers

Answer:

10t - 16

Step-by-step explanation:

4(t + 2)+ 6(t - 4)

4t + 8 + 6t -24

10t - 16

Expand the first bracket: 4t + 8
Now expand the second bracket: 6t - 24
4t + 8 + 6t - 24
Add all like terms together: 10t - 16

f(x)=x^2+6x+7
g(x)=x+2
find g(f(x))

Answers

Answer:

g(x2+6x+7)=x2+6x+9

Step-by-step explanation:

Evaluate g(f(x)) by substituting in the value of f into g

g(2x)=6(2x)−7

Multiply 2 by 6

g(2x)=12x−7

Is 3.07 the same as 3.7 ?

Answers

Answer:

yes it is a 0 is not a value if its infront of an answer

Step-by-step explanation:

no it’s not the 7 in the first on is in the hundreds place and the second is in the tenths

What is the prime factorization of 235

Answers

Answer:

5 x 47

Step-by-step explanation:

Hope this helps! <3

Answer:The prime factorization of 235 = 5•47.Step-by-step explanation:

The number 235 is a composite number because 235 can be divided by 1, by itself and at least by 5 and 47. So, it is possible to draw its prime tree.

The prime factorization of 235 = 5•47.

hope this help! ^^

david and Jack share $120 in the ratio 3:5.how much did david get ?​

Answers

Answer:

$45

Step-by-step explanation:

ratio is 3:5

David gets 3x, Jack gets 5x

So, 3x+5x=120

8x=120

x=15

David got 3x = 3*15 = $45

Answer:

45$

Step-by-step explanation:

120/8=15

15*3=45

because it is 3:5 ratio

Find the equation perpendicular to y =1/2x - 3 and goes through the point (6, -3).

Answers

Perpendicular equations have opposite reciprocal slopes, so any equation perpendicular to the equation y = 1/2 x - 2 would have the slope -2.

Now plug in the point (6, -3) into the equation y = -2x + b to find out what b is.

-3 = -2(6) + b

Multiply -2 by 6.

-3 = -12 + b

Add 12.

9 = b

So the equation is y = -2x + 9

Hope this helps

what is the mathematical sentence of "the length of wooden frame is 1foot longer than it's width and it's area is equal to 12ft²" can you translate it into quadratic equation in terms of "x"?

Answers

Answer:

x²+x+12 = 0

Step-by-step explanation:

Area if the wooden frame = ,Length ×Width

A = LW

If the length of wooden frame is 1foot longer than it's width, then;

L = W+1

Given

A = 12ft²

Substitute the derived and given parameters into the formula to have;

P = (W+1)W

12 = (W+1)W

Open the parentheses

12 = W²+W

Subtract 12 from both sides

12-12 = W²+W -12

0 = W²+W-12

Rearrange

W²+W-12 = 0

If W = x

The quadratic equation becomes:

x²+x+12 = 0

Calculate the distances from the origin to points A(11, –2, –6) and B(–3, 7, –5). Round to the nearest tenth. The distance from the origin to point A is units. The distance from the origin to point B is units. Now determine how much farther from the origin point A is than point B. Round to the nearest tenth. Point A is units farther from the origin than point B.

Answers

Answer:

Step-by-step explanation:

A(11, –2, –6) and B(–3, 7, –5) are located away from the origin (0,0,0), the points from the origin to this points is expressed as OB - OA where;

OB is the distance from the origin to the point B

OA is the distance from the origin to the point A

Using the formula for calculating distance between two points

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(-6-0)²+(-2-0)²+(11-0)²

OA = √(-6)²+(-2)²+(11)²

OA = √36+4+121

OA = √161

OA = 12.688

Similarly;

OB = √(-5-0)²+(7-0)²+(-3-0)²

OA = √(-5)²+(7)²+(-3)²

OA = √25+49+9

OA = √83

OA = 9.110

Distance from the origin to the points = 12.688 - 9.110 = 3.577

Distance from the origin to the points  ≈ 3.6 (to the nearest tenth)

Answer:

The distance from the origin to point A is 12.7 units.

The distance from the origin to point B is 9.1 units.

Point A is 3.6 units farther from the origin than point B.

An equo equila Teral Traingle has
nearest mm workout The Lower
bound of its Perimeter mcm
sides of Lenght 6.2 cm correct to

Answers

Answer:

Step-by-step explanation:

Given parameters:

Dimensions of the equilateral triangle = 6.2cm

Unknown:

Perimeter = ?

Solution:

The perimeter of the triangle is the sum of all its sides;

  Perimeter = 3(L) for an equilateral triangle;

 Perimeter  = 3(6.2) = 18.6cm

to the nearest mm = 19.0cm

HELP!!!

For which one month. What is the rate of change in rainfall amounts in Springfield the greatest?

Answers

The answer is : June & July

hope you did it!

How many miles could Katya go if she filled her 22-gallon tank? Show your math
work

Answers

Answer:

that all depends on the car mileage, say she gets 20 mpg itd be 20x22

Round 18,626,291 to the nearest million.

Answers

isn’t it 19 million?

Albert's mom has 2,523 reward points from shopping at an online store. She uses the points to buy gift cards for free cups of coffee. Each gift card costs 75 points. What is the greatest number of gift cards Albert's mom can buy? How many reward points will she have left? Use the drop-down menus to choose the numbers that make the statement true.

Answers

Answer:

Maximum number of gift cards she can purchase = 33

Reward points left with her = 48

Step-by-step explanation:

Let Albert's mom buys the number of gift cards = x

Points for each gift card = 75

Total points consumed to buy x gift cards = 75x

If total points with Albert's mom = 2523

So the remaining points with her = (2523 - 75x)

Inequality representing the remaining points will be,

(2523 - 75x) ≥ 0

75x ≤ 2523

x ≤ [tex]\frac{2523}{75}[/tex]

x ≤ 33.64

Maximum number of cards she can buy = 33

Therefore, reward points with her = 2523 - (75 × 33)

                                                         = 2523 - 2475

                                                         = 48

What are the roots of the quadratic equation y= x^2 - 10 x + 125

Answers

Answer:the roots is 2 10 and 125

Step-by-step explanation:used a caculator

Answer:

for me the answer is a but the root  is x=5+10i

Step-by-step explanation:

is this a function or not?

Answers

Answer: yes

Step-by-step explanation:

The x value does not repeat itself

find a round to the nearest tenth

Answers

Answer:

Side C= 22

Side B = 12

Side A= 22.16627

i do think it is 22.16627

Step-by-step explanation:

hope this helps

WILL MARK YOU BRAINLIEST!!!!!!

Answers

Answer:

y = 136

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle, thus

y = 82 + 54 = 136

HELP ! -4.1 , - 3.5 , 5.3 , - 1.4 order from least to greatest !!!

Answers

Answer:

-4.1, -3.5, -1.4, 5.3

Step-by-step explanation:

hope this helps!

The tables given are for the linear functions f(x) and g(x). What is the input value for which f(x)=g(x) is true?

x=____

Answers

-1, it's fairly clear just from the table...

Answer:

-1

Step-by-step explanation:

A= LWH for L
L=


What’s the answer

Answers

Answer:

A ÷ (WH)

Step-by-step explanation:

In the diagram below

Answers

Answer:

m∠A = 39°

Step-by-step explanation:

From the figure attached,

BE ≅ BC

m∠C = 32°

m∠BFD = 103°

In ΔBCE,

m∠E = m∠C = 32°  [Since, BE ≅ BC]

m∠E + ∠C + m∠EBC = 180°

32° + 32° + m∠EBC = 180°

m∠EBC = 116°

m∠EBC + m∠EBA = 180° [Linear pair of angles]

116° + m∠EBA = 180°

m∠EBA = 64°

Similarly, m∠AFB + m∠DFB = 180° [Linear pair of angles]

m∠AFB + 103° = 180°

m∠AFB = 77°

Now in ΔAFB,

m∠A + m∠AFB + m∠FBA = 180° [Sum of internal angles of a triangle = 180°]

m∠A + 77° + 64° = 180°

m∠A = 39°

7:x=2:3

What is the answer can not find out

Answers

Answer:

10.5  = x

Step-by-step explanation:

7:x = 2:3

can be rewritten as

7/x = 2/3

because, a proportion is the same as a fraction, which is the same as division

so now use cross products to solve the equations

7/x = 2/3

7 * 3 = 2 * x

simplify

21 = 2x

inverse operations

21 = 2x

/2    /2

10.5 = x

10.5

7/2 = 3.5

3.5 x 3 = 10.5

Anthony received $150 for his birthday this year. This was $10 less than
half the amount he received last year. How much money did Anthony
receive for his birthday last year? write the equation and answer

Answers

Answer:

$140

Step-by-step explanation:

150-10=140

$140

HOPEFULLY IM RIGHT!!

Have A Nice Day!!!!

:)))

Answer:
Anthony received $320 for his birthday last year.

Explanation:
What we know:
- this year, Anthony got $150
- 150=half the amount he got last year-10

We can create an equation with this information:

Let x be equal to the amount of money Anthony received last year.
150=1/2x-10

And now we solve the equation and isolate x.

150=1/2x-10
Add 10 to both sides
150+10=1/2x-10+10
160=1/2x
Divide both sides by 1/2
160/ 1/2=1/2x / 1/2
160/ 1/2=x
Dividing by a fraction is the same as multiplying its flip
160*2=x
320=x

I hope this helps! Please comment if you have any questions.

i need more help
ill give brainiest to first person to answer

Answers

steps-
-4=-4
n=-6 IS THE ANSWER

WILL MARK BRAINILIST!! Triangle PQR is transformed to triangle P'Q'R. Triangle PQR has vertices P (3, -6), Q (0, -9), and R (-3, 0). Triangle P'Q'R has vertices P'Q'R has vertices P' (1, -2), Q' (0, 3), and R' (-1, 0).

What is the scale factor of the dilation that transforms triangle PQR to triangle P'Q'R? Explain your answer.

Answers

Answer:

The dilation is 3 times smaller of divided by 3.

Step-by-step explanation:

If you look at each beginning point all the numbers are divisible by 3 then when you look at the ending points they are the same as the beginning just 3 times smaller.

Answer:

The dilation is 3 times smaller of divided by 3.

Step-by-step explanation:

If you look at each beginning point all the numbers are divisible by 3 then when you look at the ending points they are the same as the beginning just 3 times smaller.

Step-by-step explanation:

Name the constant of variation for the equation: y=-2/3x

Answers

The constant of variation is the slope, which is the number before the x variable.

The answer is -2/3

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