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

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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:

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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.

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Graph the arithmetic sequence -1,-3,-5,-7,

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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

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

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Answer:

Step-by-step explanation: it’s 41%

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

Please help!
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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:

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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

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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

Will give brainliest!

ABC and DEF are similar triangles. If the side lengths of ABC are 6, 8, and 12, and the
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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

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Find x using 6/x = 12/18:

6/x = 12/18

Cross multiply

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Find x using 8/y = 12/18:

8/y = 12/18

Cross multiply

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

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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

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Step-by-step explanation:

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Answer:

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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.

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

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Answers

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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If you need another explanation comment on this one

Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answer:

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Answer:

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Step-by-step explanation:

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This is properly represented as:

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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 = ?