You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measures of the interior angles of the triangle.

Answers

Answer 1

Answer:

Step-by-step explanation:

A linear pair are two given angles whose sum is equal to [tex]180^{o}[/tex].

Let the exterior angle be represented by [tex]x^{o}[/tex], and the three interior angles of the triangle be represented by [tex]a^{o}[/tex], [tex]b^{o}[/tex] and [tex]c^{o}[/tex].

Assume that the vertex angle [tex]c^{o}[/tex] is the linear pair to the exterior angle [tex]x^{o}[/tex].

i.e            [tex]x^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex]  (sum of angles on a straight line)

Thus,

i. [tex]a^{o}[/tex] +  [tex]b^{o}[/tex] = [tex]x^{o}[/tex]  (sum of two opposite interior angles is equal to an exterior angle)

⇒ [tex]a^{o}[/tex]  = [tex]x^{o}[/tex] - [tex]b^{o}[/tex]

Also,

[tex]b^{o}[/tex]  = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]

But,

[tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex]   (sum of angles in a triangle)

⇒ [tex]c^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]a^{o}[/tex] +  [tex]b^{o}[/tex])

and

[tex]a^{o}[/tex] + [tex]b^{o}[/tex] = [tex]180^{o}[/tex] - [tex]c^{o}[/tex]

ii. [tex]a^{o}[/tex] + [tex]b^{o}[/tex] + [tex]c^{o}[/tex] = [tex]180^{o}[/tex]   (sum of angles in a triangle)

[tex]a^{o}[/tex] = [tex]180^{o}[/tex] - ([tex]b^{o}[/tex] + [tex]c^{o}[/tex])

Also,

[tex]a^{o}[/tex] +  [tex]b^{o}[/tex] = [tex]x^{o}[/tex]

⇒ [tex]b^{o}[/tex] = [tex]x^{o}[/tex] - [tex]a^{o}[/tex]

[tex]c^{o}[/tex] = [tex]180^{o}[/tex] - [tex]x^{o}[/tex]


Related Questions

Fernando is starting a new sales job and needs to decide between two different salary plans. For Plan A, he will earn $100/week plus 15% commission on all sales. For Plan B, he will earn $150/week plus 10% commission on all sales. For what amount of weekly sales are the two plans equal?

Answers

Answer:

At 10 weeks

Step-by-step explanation:

100+15x=150+10x

15x=50+10x

5x=50 divided both sides by 5 and x=10

Simplify the expression by adding or subtracting the linear expressions. 9x - 20 - 8x + 2 *
-11x - 6
17x - 18
x -18
22x + 17

Answers

Answer:

9x - 20 - 8x + 2 * -11x - 6 +17x - 18 +x -18 +22x + 17

If you mean so, then this is the answer

19x-45

Helpppppp plzzz nowwww

Answers

5.7 i believe is the answer

Answer: side AB is 5.7 units

Step-by-step explanation:

If you look at the congruence marks on the angles, you can see that side AB and side KL correspond. Since we know KL is 5.7, AB must be 5.7 as well. :)

Which statement is correctly written as a conditional statement?

A) Any four-sided shape is a quadrilateral.
B) A shape has four sides when it is a quadrilateral.
C) If a shape has four sides, then it is a quadrilateral.
D) A shape has four sides, or it is a quadrilateral.

Answers

Answer:

C

Step-by-step explanation:

If a shape has four sides, then it is a quadrilateral.

If a shape has four sides, then it is a quadrilateral so option (C) will be correct.

What is quadrilatereal?

A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.

In other meaning, a quadrilateral is a kind of polygon in which four sides for example rectangle, square, and parallelogram are quadrilateral.

a quadrilateral is a four-sided polygon, having four edges and four corners

A parallelogram is a basic quadrilateral with two sets of parallel sides.

The confronting or opposing sides and the opposing angles of a parallelogram are of equal length.

A quadrilateral is a quadrilateral because it has four sides not because it is quadrilateral so it has four sides.

For example, 4 sides are equal so the square is not due to the square all lines will same.

Hence If a shape has four sides, then it is a quadrilateral.

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I need help with my spanish


Can someone pls help

Answers

Answer:

It finally let me make an answer so here’s the answer:

1) he goes to el heladeria to get more ice cream

2) el banco to get money to pay

4) el mercado to get vegetables

5) el cafe to get more bread

The things you circle in the sentence for the correct verb are

1) comer (eat)

3) beber (drink)

4) usar (use)

5) comer (eat)

6) beber (drink) I hope this helps!

-28+4x=4(x-7) how many solutions marking brainlest

Answers

Answer:

x^2 + 5 x + =0

Step-by-step explanation:

We need to factor this trinomial by grouping.

The first step in this process consists of splitting the middle term into two terms.

In our example, 5x  has been split into 2x and .

Notice that one common factor can be factored from the first 2 terms, and another from the second 2 terms

There were 20 cups of pudding left in the cafeteria after lunch. The lunch aide poured the extra pudding into quart sized containers how many quart sized containers will she need?

Answers

Answer:

5

Step-by-step explanation:

1 galon =16 tazas

1/4 de galon=4 tazas

1+.25= 1.25 ó 1+1/4=1, 1/4 y eso lo multiplico por 4

1.25 ×4= 5

The lines below are parallel. If the solid line has a slope of 1, what is the
slope of the dashed line?

Answers

Answer:

The lines below are parallel. If the slope of the solid line is –3

Step-by-step explanation:

Which of the following is equivalent to 8^(1/3)?
Option 1
Option 2
Option 3
Option 4
(look at photo for answers)

Answers

the answer is option 2....

Answer:

Option 2

Step-by-step explanation:

when the power appears as a fraction, take the root of the number based on the denominator of the fraction when numerator is equal to 1

7(x + 4) = -21 what is x in this problem?

Answers

X=-7
Sorry I can’t explain it! My device is really slow right now!

Answer:

-7

Step-by-step explanation:

7x+28=-21

7x=-49

x=-7

Quadratic functions q and ware graphed on the same coordinate grid.
The vertex of the graph of g is 18 units below the vertex of the graph of w.
Which pair of functions could have been used to create the graphs of q and w?

Answers

Answer:q(x)=18x^2 and W(X) = x^2

Step-by-step explanation:

The pair of functions that used for developing the graph of g and w is [tex]q(x)=18x^2\ and\ W(X) = x^2[/tex]

What is the vertex of the parabola?

The vertex of a parabola should be the point where the parabola crosses its axis of symmetry. In the case when the coefficient of the x2 term is positive, so the vertex will be the lowest point on the graph.

Since The vertex of the graph of g is 18 units below the vertex of the graph of w so the above functions should be considered.

Therefore, The pair of functions that used for developing the graph of g and w is [tex]q(x)=18x^2\ and\ W(X) = x^2[/tex]

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distributive property is a property of equality
A) true
B) false

Answers

Answer:

The distributive property states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum.

Name a line containing point V.

Answers

Answer:

Line A

Step-by-step explanation:

AAnswer:

Step-by-step explanation:

Marco is 6 feet 3 inches tall. There are 2.54 centimeters in 1 inch. What is Marco's height in centimeters?

Answers

Answer:

192 cm

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, let's convert 6 feet 3 inches to just inches. Because there are 12 inches in 1 foot, we can say that there are 72 inches in 6 feet. Combined with the other 3 inches, we can say that Marco is a 75 inches tall.

Now, we can multiply the number of inches we found by 2.54 to get Marco's height in centimeters. This gives us 190.5 cm.

Which expression is equal to (x+2)(x-4)/(x-4)(x+4)

A) x-2/x+4

B) x+4/x+2

C) x-2/x-4

D) x+2/x+4

Answers

Answer:

The expression equal to [tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}[/tex] is [tex]\frac{(x+2)}{(x+4)}[/tex]

Option D is correct.

Step-by-step explanation:

We need to solve the expression [tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}[/tex]

Since it is a fraction, and all terms are multiplying with each other we can cancel out common terms.

Since x-4 is both in numerator and denominator so, it will be cancelled out and we will get:

[tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}\\=\frac{(x+2)}{(x+4)}[/tex]

So, the expression equal to [tex]\frac{(x+2)(x-4)}{(x-4)(x+4)}[/tex] is [tex]\frac{(x+2)}{(x+4)}[/tex]

Option D is correct.

Answer:

D.) x+2/x+4

I took the quiz :)

Step-by-step explanation:

What is the value of the expression shown below (3/5)^2+4×3-2 PLZ HELP THIS ASSIGNMENT IS DUE IN 10 MINUTES ​

Answers

Answer:

[tex]10\frac{9}{25}[/tex]

Step-by-step explanation:

Answer:

10 9/25

Step-by-step explanation:

i did mathsss i hope this does help tho

4v + 4(v + 10) = -2v - 20

Answers

V =-6 bc I distribute 4 into v+10 and go 4v+10 and add the same numbers and subtract both side and add both side to get v alone and divided 10v into -60 so the answer is v=-6

.MARY WAS TOLD TO RUN AROUND THE TRACK 5 TIMES BY HER COACH. ONCE AROUND THE TRACK IS 5/6 OF A MILE. MARY WAS ONLY ABLE TO RUN AROUND THE TRACK 4 1/3 TIMES. HOW MANY MILES TOTAL DID MARY RUN?

Answers

Answer:

3.61 miles

Step-by-step explanation:

Given that:

Length of track = 5/6 of a mile

Number times Mary was able to run around the track = 4 1/3 times

Total miles ran by Mary :

(Equivalent mile of the track * number of times Mary ran around the track)

5/6 of a mile * 4 1/3 times

5/6 * 13/3

= 65 / 18

= 3.611111 miles

Hence, total Number of miles ran by Mary is 3.61 miles

Which of the following is equivalent to the fraction above? -(3/16)
A. 6/13
B. -13/6
C. -6/-13
D. -6/13

Answers

Answer:

c

Step-by-step explanation:

Answer:

D. -6/13

Step-by-step explanation:

Charlotte is working two summer jobs, making $21 per hour tutoring and $14 per hour clearing tables. Last week Charlotte worked twice as many hours tutoring as she worked hours clearing tables hours and earned a total of $168. Graphically solve a system of equations in order to determine the number of hours Charlotte worked tutoring last week, x,x, and the number of hours Charlotte worked clearing tables last week, yy.

Answers

Answer: this is the answer please follow to the explanation

Step-by-step explanation:

21x + 14y = 168. X=2y

14y = -21x +168. 2y=x

14 divided by 14 on one side and

-21 + 168 divided by 14 on the other side

You should get...

Y= -3/2x +12

For part 2 where they want you to put the 2 numbers in, you should put the point they intercept which is (6,3).

Well, have a good day

Which of the following ordered pairs is a possible solution to the equation y = 3x - 2?

Answers

Answer:

D) (1,1)

Step-by-step explanation:

You can find the solution by plugging the x-value of each coordinate into the equation. It will be a solution if the y-value of the equation equals the y-value of the coordinate.

For example:

y = 3x -2

y = 3(1) - 2

y = 3-2

y = 1

1 = 1

(1, 1) are the coordinates that are on the given line.

What are coordinates?

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given a equation y = 3x -2

To find which coordinates will satisfy the equation:

For coordinates (2, 0)

at x = 2, y should be zero

y = 3 * 2 -2

y = 4

Not satisfied

For coordinates(-3, 0)

at x = -3, y should be 0

y = 3 * -3 - 2

y = -9 -2

y = -11

Not satisfied

For coordinates(0, 2 )

at x = 0, y should be 2

y = 3*0 -2

y = -2

Not satisfied

For coordinates(1, 1)

at x = 1, y should be 1

Y = 3*1 - 2

y = 3 - 2

y = 1

satisfied

Therefore, (1, 1) are the coordinates that are on the given line.

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What do you call the pairs of roots of quadratic
equation with complex solutions?
Math

Answers

Imaginary numbers
Imaginary numbers contain complex solutions (a +- bi)

Jen walked 1/4 of a mile in 1/2 of an hour. At this rate, how long will it take her to walk 2 miles to the park?
A. 2 hours
B. 8 hours
C. 4 hours
D. 6 hours​

Answers

Answer:

The awnser is C. 4 hours

Step-by-step explanation:

It takes her 2 hours two walk 1 mile so 2*2 is 4

the value of y varies directly with x. when y = 7.5, x = 5. what is the value of y when x = 80?.

Answers

Answer:

Step-by-step explanation:

120 = y. the ratio is 3:2

80/2 is 40

40 times 3 is 120

120:80 = 3:2

the area of a rectangle is 177 square meters the width is 9 meters what is the length of the rectangle

Answers

Answer:

19.67

Step-by-step explanation:

divide 177 by 9. the answer is 19.66666667, but you might have to round ;)

x+2=18
3(x+2)=18
How can we get Equation B from Equation A?

Answers

Answer:

x+2 = 18  

x = 18-2

x=16

3(x+2) =18

3x + 6 =18

3x = 18 -6

3x = 12

x = 12/3 = 4

Step-by-step explanation:

mx = pn , for x
Someone pleaseeeee help

Answers

Answer:

x=pn/m

Step-by-step explanation:

Divide both sides by m to isolate x from the other variables.

mx/m = pn/m

cancel out the m where possible.

x = pn/m

She visited Creepy Cavern at (-2, 5), Bernie's Barn at (-3, 2), Sweet Symphonies at (-3, -1), Rock and Roll Hall at (-2, -4), Whimsical Wonders at (3, -4), Mystery Mansion at (3, 2), and Star Gazing Point at (5, 5). Which of these pairs of places are more than 6 units from one another?

Answers

Answer:

We need to find the distance between the pairs of points to know which is greater than 6units. To do that we make use of this formula:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Where [tex](x_1 , y_1)[/tex] and [tex](x_2 , y_2)[/tex] are two points on the line.

Let us denote Creepy Carven with CC, Bernie Barn as BB, Sweet Symphonies as SS, Rock and Roll Hall as RR, Whimsical Wonders as WW, Mysterial Mansion as MM and Star Grazing point as SG.

The distance between CC (-2, 5) and BB(-3, 2) using that formula will be:

[tex]d = \sqrt{(-3 + 2 )^2 + (2 - 5)^2}[/tex]

Which is [tex]d = \sqrt{(-1 )^2 + (-3)^2}[/tex]

That gives

[tex]d = \sqrt{10} < 6[/tex]

If we do this for BB to SS we have our value greater than 6, SS to RR our value greater than 6, RR to WW greater than 6, WW to MM is equal to 6 and MM to SG is less than 6.

From here we conclude that the pairs of places greater than 6 is:

BB to SS

SS to RR

RR to WW

WW to MM

Answer:

First, plot each of the points and label them.

Determine the distance between the pairs of places listed in each answer choice.

Since Whimsical Wonders and Rock and Roll Hall lie on the same horizontal line, the distance between the two points is the absolute value of the difference of the x-coordinates.

Using this same process, the distance between Bernie's Barn and Mystery Mansion is 6 units, and the distance between Creepy Cavern and Star Gazing Point is 7 units.

Since the Mystery Mansion and Whimsical Wonders lie on the same vertical line, the distance between the two points is the absolute value of the difference of the y-coordinates.

Using this same process, the distance between Rock and Roll Hall and Creepy Cavern is 9 units, and the distance between Sweet Symphonies and Bernie's Barn is 3 units.

Therefore, the pairs of places that are more than 6 units from one another are Creepy Cavern and Star Gazing Point and Rock and Roll Hall and Creepy Cavern.

Step-by-step explanation:

Find the total surface area of the
following square pyramid:
10 cm
12 cm
SA = [?] cm2

Answers

Step-by-step explanation:

Hope this helps, happy learning!!!!

The surface area of the square pyramid will be 240 square centimeters.

What is Geometry?

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The dimension of the square pyramid will be 12 cm and 10 cm.

Then the surface area of the square pyramid will be

The surface area is four times the area of the triangle.

Surface area = 4 x 1/2 x 12 x 10

Surface area = 2 x 120

Surface area = 240 sqaure cm

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Solve for x

3x−8≤23 AND −4x+26≥6

Answers

Answer:

Step-by-step explanation:

Ok so the first one is X<31/3

And the second one is X>-5

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