In a kite ABCD, AB=CB , AD = CD, <B= 115 degree, <D=30 degree. Find <A = ?

Mathematics High School

In a kite ABCD, AB=CB , AD = CD, <B= 115 degree, <D=30 degree. Find <A = ?

Answers

Answer 1

Answer:

The measure of ∠A = 107.5°

Step-by-step explanation:

Given that

ABCD is a kite such that

AB = BC and AD = DC

Join A and C

Since AB = BC

→ ∠BAC = ∠BCA

Since , the angles opposite to equal sides are equal.

Let ∠BAC = ∠BCA = x°

and

Since AD = DC

→ ∠CAD = ∠ACD

Since , the angles opposite to equal sides are equal.

Let ∠CAD = ∠ACD = y°

Now

In ∆ ADC ,

∠ADC + ∠CAD + ∠ACD = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 30° + y°+ y° = 180°

⇛ 30°+2y° = 180°

⇛ 2y° = 180°-30°

⇛ 2y° = 150°

⇛ y° = 150°/2

⇛ y° = 75°

Therefore, ∠CAD = ∠ACD = 75°

and

In ∆ ABC,

∠ ABC + ∠BAC + ∠BCA = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 115° + x° + x° = 180°

⇛ 115°+2x° = 180°

⇛ 2x° = 180°-115°

⇛ 2x° = 65°

⇛ x° = 65°/2

⇛ x° = 32.5°

Therefore, ∠BAC = ∠BCA = 32.5°

Now, ∠ A = ∠BAC + ∠CAD

⇛ ∠A = 32.5° + 75°

⇛ ∠A = 107.5°

Therefore, ∠A = 107.5°

Answer:-

) The measure of ∠ADC = 145°) The measure of ∠A = 107.5°

Read more:

Related Questions

Write an algebraic expression to represent the verbal statement: The product of the difference of m and 7 and 6.

Answers

Answer:

(m-7) * 6

Step-by-step explanation:

you follow the statement from left to right. You see that there's a product so you write a product sign

then you know its the difference of m-7 on one side and 6 on the other getting

(m-7) * 6

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Answers

Answer:

389.9 to 1 decimal place

If you need another explanation comment on this one

Step-by-step explanation:

the surface area (base area plus side wall) of a cone is, when we have the radius and the length of the slanted side wall :

SA = pi×r×(r + l)

in our case here

r = half of the diameter = 12/2 = 6 m

l = 13.4 m

so, we have

SA = pi×6×(6 + 13.4) = pi×6×19.4 = 365.6813849... m²

What is the slope of the line whose equation is 12=4x−6y?

Please and thanks if you decide to answer.

Answers

Answer:

slope =4

Step-by-step explanation:

from, y=mx + c

where m is slope

Answer:

the slope formula is y=mx+b where b is the y intercept and m is the slope we rewrite the equation by subtracting 4x from either side and then dividing both sides by 6 so we have y=-0.6x+2 so m the slope is -0.6

need help with pre-cal please

Answers

Answer:

x = n² ± n√(n² + 8)

Step-by-step explanation:

x ≠ 0, n ≠ 04/x² + 1/x = 1/(2n²)(x + 4)/x² = 1/(2n²)2n²(x + 4) = x²x² - 2n²x - 8n² = 0D = (-2n²)² - 4(-8n²) = 4n⁴ + 32n² = 4n²(n² + 8)x = (2n² ± 2n√(n² + 8))/2x = n² ± n√(n² + 8)

What does the rational form of the ratio a:b look like?

Answers

The rational form of a ratio is the ratio represented as a fraction (or quotient)

The rational form of the ratio a : b is a/b

The ratio is given as a : b (pronounced a ratio b)

This is properly represented as:

[tex]\mathbf{Ratio = a : b}[/tex]

To convert to rational form, means that we express the ratio as a fraction.

So, the ratio becomes

[tex]\mathbf{Ratio = \frac a b}[/tex] (pronounced a divided by b)

Hence, the rational form of the ratio a : b is a/b

Answers

Answer:

p(7) = 57

Step-by-step explanation:

Because this is a function, all you have to do is input 7 for x like so:

p(x)=x^2+x+1 ---------------> p(7)=7^2+7+1

so 49 + 8

= 57

Find the gradient of the line segment between the points (6,-4) and (10,-10). Give your answer in its simplest form.

Answers

Answer:

To calculate the gradient of a straight line we choose two points on the line itself. The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates).

so it is 0.2

− 11/12 + p = 1/6

what does p =

Answers

Answer:

13/12

Step-by-step explanation:

p=1/6+11/12=(2+11)/12=13/12

[tex]⇒ - \frac{11}{12} + p = \frac{1}{6} \\ p = \frac{1}{6} + \frac{11}{12} \\ p = \frac{2 + 11}{12} \\ p = \frac{13}{12} [/tex]

2 iPhones cost $1,680, how much would 10 iPhones cost?

Answers

Answer:

$8,400

Step-by-step explanation:

one way to solve it would be that since you know 2 x 5 = 10 you can do $1,680 x 5 and that = $8,400

No links No Files Need help ASAP

Answers

Answer: 6

Step-by-step explanation: I think think the answer is 6 because if you cut 6 in half you get 3 and if cut 4 in half u get 2 the mutiply them...dont get mad if it wrong

Answer: A = 24 units^2

Step-by-step explanation: If you cut the shaded region in half it's two rectangles so you have to find the area of it using the formula to find the area of a rectangle.

A = (w)(l) A = (6)(4) A = 24 units^2

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30 and 60

Answers

Answer:

GCF of 30 and 60 is 30.

Step-by-step explanation:

The volume of a cylinder closed at the one end is 1056cm cube. If its height is 21cm, and the radius is 4, find the total surface area

Answers

Answer:

578 cm^2

Step-by-step explanation:

The surface area is given by one circle of radius 4 (the other is missing!), plus a "rectangle" (the lateral surface) of sides 21 and [tex]2\pi \times 4[/tex] (the length of the circumference at the base). Adding them up we get:[tex]\pi \times4^2 + 21\times 2\pi\times4 = 184\pi \approx 578 cm^2[/tex]

Twice a number diminished by seven

A) 7x - 2
B) 2x + 7
C)2x - 7
D) 7x + 2

PLZ HELP IM NOT SURE WITH MY ANSWER π-π

Answers

Answer:

2x-7

Step-by-step explanation:

let the no be X

twice the no =2X

diminished by 7= 2X-7

Answer:

C)2x - 7..................

The sides forming the right angles and hypotenuse of a right angled triangle are x cm, (2x + 2) cm and (3x – 2) cm respectively. Calculate the perimeter of the triangle.

Answers

Answer:

Step-by-step explanation:

Perimeter is the sum of all the sides:

(x) + (2x + 2) + (3x - 2)

Add like-terms:

6x + 2 - 2 = 6x

Perimeter = 6x

Please help!
.
.
.
.
.

Answers

Answer:

Step-by-step explanation:

To calculate the value of x we must first understand the total value of all angles in a triangle.

Sum of all angles in a triangle = 180 degrees

That said, we need to write an equation for the total number of degrees in the triangle and solve for x

This will be as follows:

(13x+2)+(5x-7)+(3x-4)=180

The we combine the like terms. This will be as follows:

(13x+5x+3x)+(2-7-4)=180

Simplify further to get

21x-9=180

Simplify further by collecting all like terms on one side of the equal. This will entail the addition of 9 on each side of the equal sign as follows:

21x-9+9=180+9

you will find 21x=189

Simplify further by dividing both sides of the equal sign by 21 to solve for x

21x/21=189/21

Therefore x=9

pls help i dont get it

Answers

Answer:

Step-by-step explanation: it’s 41%

plz help i will give brainiest
Graph the arithmetic sequence -1,-3,-5,-7,

Answers

Answer:

going up by 2 numbers

Step-by-step explanation:

Going up by -2 for example from 1 to -1 you are go up by -2

please help will mark as brainlist

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Answer:

176

Step-by-step explanation:

Answer:

[tex]m[/tex]∠STV = 43°

Step-by-step explanation:

It has the corresponding relation with ∠UTV

Five less than five times a number is less than six times the same number plus
2.

Answers

Answer:

See below:

Step-by-step explanation:

Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day.

We can solve this problem in one single step, I'll start off with that.

We can first figure out what it says and make an algebraic equation. We can see what language the question uses and elaborate on that to create our equation.

[tex]5x-5<6x+2[/tex]

We can use algebra to simplify the equation so that we can solve for it.

[tex]-5<x+2\\-7<x\\x>-7[/tex]

We can check if this is correct by testing a few numbers from that range, I'll take -5 and 2.

[tex]5(2)-5<6(2)+2?\\10-5<12+2?\\5<14[/tex]

We've proven that 2 is working.

[tex]5(-5)-5<5(-5)+2?\\-25-5<-25+2?\\-30<-23[/tex]

We've also proven that -5 works.

We can now say that we've solved the problem, the solution of the problem would be x>-7.

Cheers!

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Answers

Answer:

(4, 4)(4, -4)

Step-by-step explanation:

The solution is the point of intersection of the two lines on the graph.

Graph 1.

The lines intersect at (4, 4). The solution is (x, y) = (4, 4).

Graph 2.

The lines intersect at (4, -4). The solution is (x, y) = (4, -4).

please , answer this question:(

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Answer:

50s

Step-by-step explanation:

To find algebraic expression, you need to look at the paragraph

Cost of 1 gift card of music : $50Cost of each song : s dollars

We have to multiply 50 by s dollars.

Factories often add filler when making meatballs sold by the bag. One factory obtained 72 kg of beef from overseas. They want to add 1.2 oz of filler for each
pound of beef, How many ounces of filler will the factory need in order to make meatbälls out of this shipment of beef? Help

Answers

Answer:

158.732829

rounded up: 159

Step-by-step explanation:

trust the calculator

X^2+5*x^3+7
Solve pls lol

Answers

don't know sorry

Step-by-step explanation:

sorry very very school

Answer:

5x^3+x^2+7

Step-by-step explanation:

Write the given expanded form into the standard form of a number.

4
4
T-Th + 5
+

5
T + 1
+

1
H-Th + 9
+

9
O + 3
+

3
M + 7
+

7
Th

Answers

Answer

44,005 + 5,001+ 100,009 + 93 + 3,000,007+ 7,000

Step-by-step explanation:

Is 3 a divisor of 51?

Explain why it is or why it’s not.

Answers

Answer:Yes

Step-by-step explanation:

A shortcut to tell whether a whole number is divisible by 3 is to add its digits together and see if the result is divisible by 3.

Answer:

yes 51 divided by 3 equals 17 there is no remainder

hsbhjbhfbghwebfhdfbghef gbhbr ghb erhjtgb

Answers

Answer:

the answer to hsbhjbhfbghwebfhdfbghef gbhbr ghb erhjtgb is hdshdjsh df ejnjg grkejfiejfirnigjre

Step-by-step explanation:

you have to multiply hsbhjbhfbghwebfhdfbghef gbhbr ghb erhjtgb by skjdkahdjhs to get jskhijdfkjd then multiply it by sijdikjakdj9uie. the answer would be hdshdjsh df ejnjg grkejfiejfirnigjre.

what is 4 1/2 - 1
8/10= in Fractions

Answers

[tex]4\frac{1}{2} - 1\frac{8}{10} = \frac{9}{2}- \frac{9}{5} = \frac{27}{10}[/tex]

ok done. Thank to me :>

Answer:

4 1/2= 9/2

1 8/10= 18/10= 9/5

9/2-9/5=

(45-18) /10=

27/10 or 2 7/10

Step-by-step explanation:

Help me please!!!!!!!!!

Answers

Answer:

X=5

Step By Step:

Will give brainliest!

ABC and DEF are similar triangles. If the side lengths of ABC are 6, 8, and 12, and the
longest side of DEF is 18, then what are its other side lengths?
9 and 14
9 and 12
14 and 16
24 and 36

Answers

Applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Properties of Similar Triangles:

The ratio of the corresponding sides two triangles that are similar to each other are the same/equal.

Given that ΔABC and ΔDEF are similar triangles, therefore:

Let, a = 6, b = 8, and c = 12 be the sides of ΔABC.Let, x, y, and z be the sides of ΔDEF.Let z = 18

Thus:

a/x = b/y = c/z

Substitute

6/x = 8/y = 12/18

Find x using 6/x = 12/18:

6/x = 12/18

Cross multiply

x = [tex]\frac{18 \times 6}{12}[/tex]

x = 9

Find x using 8/y = 12/18:

8/y = 12/18

Cross multiply

x = [tex]\frac{18 \times 8}{12}[/tex]

x = 12

Therefore, applying the properties of similar triangles, the other side lengths of ΔDEF are: B. 9 and 12

Learn more about similar triangles on:

https://brainly.com/question/11899908

The sum of two consecutive odd numbers is 52.Using an algebraic equation
find the two odd numbers.

Answers

Answer: 25, 27

Step-by-step explanation:

52=x+x+2=50=2x=x=25

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In a kite ABCD, AB=CB , AD = CD, <B= 115 degree, <D=30 degree. Find <A = ?​

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In a kite ABCD, AB=CB , AD = CD, <B= 115 degree, <D=30 degree. Find <A = ?