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:

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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

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Find x using 6/x = 12/18:

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Find x using 8/y = 12/18:

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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

No links No Files Need help ASAP

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If you need another explanation comment on this one

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

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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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Answers

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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.

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

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Answers

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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

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Answers

Answer:

(m-7) * 6

Step-by-step explanation:

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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

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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.

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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:

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

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Answer:

Step-by-step explanation: it’s 41%

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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 = ?