1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kifflom [539]
3 years ago
5

Topic 6: Kites (Gina Wilson, Geometry)

Mathematics
1 answer:
sergey [27]3 years ago
4 0

Answer:

35.

So that we have:

KLN = 54          JKN =36

LKN = 72          NMJ = 18

KNM = 126       JLM = 72

LJM = 90          KLM = 126

36.

CE = 6√13

37.

m∠Z = 88°

38.

m∠GFE = 85

Step-by-step explanation:

35.

As KLMN is a kite:

+) KL = KN

=> Triangle KLN is  an isosceles triangle.

=> m∠KLN = m∠ KNL = m∠KNJ = 54°

In triangle KLN, total measure of three internal angles are 180 degree, so that: m∠KLN + m∠ KNL + m∠ LKN = 180°

=> 54 + 54 + m∠ LKN = 180°

=> m∠ LKN = 180 - 54 - 54 = 72°

+) KM is the bisector of both Angle LKN and Angle LMN

So that we have:

  • m∠JKN = 1/2 m∠LKN = 1/2 * 72 = 36°
  • m∠NMJ = 1/2 m∠LMN = 1/2 * 36 = 18°

+) KM and LN is perpendicular to each other at point J

=> m∠LJM = 90°

+) m∠KLM = m∠KNM; m∠KLM + m∠KNM + m∠LKN + m∠LMN = 360°

=> m∠KLM + m∠KLM + 72 + 36 = 360

=> 2 m∠KLM = 360 - 72 - 36 = 252

=> m∠KLM = 252/2 = 126 = m∠KNM

+) We have: m∠KLM = m∠KLN + m∠JLM

=> m∠JLM = m∠KLM - m∠KLN = 126 - 54 = 72

36.

As BCDE is a kite, we have:

+) BC = BE; CD = DE = 21

+) BD is perpendicular to CE and intersect each other point F

=> Angle CFD = 90

=> Triangle CFD is the right triangle

According to Pythagoras theorem: CF^2 + DF^2 = CD^2

=> CF^2 = CD^2 - DF^2  = 21^2 - 18^2 = 441 - 324 = 117

=> CF = \sqrt{117} =3\sqrt{13}

+) According to the feature of a kite shape, F is midpoint of CE

=> CF = FE = 1/2 x CE

=>CE = 2 x CF = 2 x 3\sqrt{3} = 6 \sqrt{13}

So that CE = 6√13

37.

As given, WXYZ is a kite shape.

According to the feature of a kite shape, angle ZWX and angle ZYX are equal to each other.

=> ∠ZWX = ∠ZYX

=> 8x -23 = 6x +11

=> 8x - 6x = 11 + 23

=> 2x = 34

=> x = 34/2 = 17

=> ∠ZWX = 8x - 23 = 8*17 - 23 = 113°

=> ∠ZWX = ∠ZYX = 113°

As WXYZ is a kite shape, so that total measure of 4 internal angles of it are 360 degree

So that we have:

∠Z + ∠ZWX + ∠ZYX + ∠WXY = 360

=> ∠Z + 113 + 113 + 46 = 360

=> ∠Z = 360 -113 -113-46 = 88°

So that the measure of ∠Z is 88°

38.

As GDEF is a kite shape. As we can see, GE is the longer diagonal, so that it is the bisector of both Angle DGF and Angle DEF.

H is on GE and GE is the bisector of Angle DEF, so we have:

m∠HEF = m∠GEF = 1/2. m∠DEF = 1/2 . (12x- 16)= 6x - 8

As GDEF is a kite shape so that the two diagonals DF and GE are perpendicular to each other, so that: m∠EHF = 90

In the triangle EHF, m∠EHF = 90

=> EHF is a right triangle

=> m∠HEF + m∠EFH = 90

=> 6x - 8 + 3x -1 = 90

=> 9x = 90 + 8 + 1 = 99

=> x = 99/9 =11

=> m∠HEF = 6x - 8 = 6*11 - 8 = 58 = m∠GEF

GE is the bisector of both Angle DGF

=> m∠EGF = 1/2. m∠DGF = 1/2 . 74 = 37

In the triangle GEF, total measure of three internal angles are 180

=> m∠GFE + m∠EGF + m∠GEF = 180

=> m∠GFE + 37 + 58 = 180

=> m∠GFE = 85

You might be interested in
Find the value of the missing coefficient in the factored form of 8f^3-216g^3
adoni [48]

Answer:

The value of the missing coefficient is 12

Step-by-step explanation:

* Lets explain how to factorize the difference of two cubes

- The factorization of the difference of two cubes like a³ - b³, is a

  product of a binomial and trinomial

- The binomial is the cube root of the first term and the second term

∵ The ∛a³ = a and ∛b³ = b

∴ The binomial is (a - b)

- We will find the trinomial from the binomial by square the 1st term

 of the binomial and multiply the 1st term and the 2nd term of the

 binomial with opposite sign of the binomial and square the 2nd

 term of the binomial

∴ The trinomial is (a² + ab + b²

∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)

* Lets solve the problem

∵ 8f³ - 216g³ is the difference of two cubes

∵ ∛(8f³) = 2f

∵ ∛(216g³) = 6g

∴ The binomial is (2f - 6g)

- Lets make the trinomial

∵ (2f)² = 4f²

∵ (2f)(6g) = 12fg

∵ (6g)² = 36g²

∴ The trinomial = (4f² + 12fg + 36g²)

∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)

∴ The value of the missing coefficient is 12

7 0
3 years ago
What is the best approximation for the area of this circle?
Svetradugi [14.3K]
Area of circle = πr² = 3.14×4² = 50.24m²

The best approximation is C.
6 0
3 years ago
Read 2 more answers
A frame is marked down by 22 percent from an original price of $14.50. What is the new price?
Valentin [98]
22% = 22/100 22/100 * 14.50 = 3.19 (this is the amount discounted off original price) 14.50 - 3.19 = $11.31
7 0
3 years ago
Read 2 more answers
State the property.<br>4(2+3)=(2+3)4​
Komok [63]

Hmm, it looks like it could be commutative property of multiplication.

The order of the expression is different.

4(2+3)=

4(5)=20

(2+3)4=

(5)4= 20

8 0
3 years ago
Help pls i need this done tonight i dont have much longer
zvonat [6]
Answer:
Jessica wants 180 plants in her garden.

Step-by-step explanation:
The formula for the area of the triangle is (1/2)*base*height.
So here, Let’s say 8 feet is the base and 15 feet is the height.
the area of the triangle would be (1/2)*8*15. That equals 60 square feet.
If Jessica wants 3 plants each square foot, then 60*3, which is 180 plants.

Note: * means the multiplication sign.
7 0
2 years ago
Read 2 more answers
Other questions:
  • Which expression is equivalent to -3x+24? Select two answers!
    13·1 answer
  • When the perimeter of a rectangle is 68ft. and the ratio of it's length to it's width is9:8. What are the dimensions of the rect
    8·2 answers
  • Consider the following quadratic equation: 25x2=36 Using the standard form ax2+bx+c=0 of the given quadratic equation, factor th
    14·1 answer
  • Which The number 15,247<br>are 15,274 is greater ? use the symbol (&lt;or&gt;)​
    13·2 answers
  • Convert.<br> 300 liters<br> to hectoliters
    6·2 answers
  • if the points (2,-3) , (8,3) and (4,7) are the vertices of triangle ,find the coordinate of the middle point of the sides of the
    10·1 answer
  • 2b-m=5 what is the solution for m
    15·1 answer
  • Is the answer option c?
    11·1 answer
  • Find the value of +x18 when =x8.
    12·2 answers
  • What is the slope of the line passing through points A and B?<br> A -2 <br> B -1/2<br> C 1/2<br> D 2
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!