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Lostsunrise [7]
2 years ago
10

Determine all missing angles below.

Mathematics
1 answer:
jekas [21]2 years ago
7 0

Answer:

  a = 60, b = 19, c = 101, d = 79, e = 50

Step-by-step explanation:

Relations that are helpful here are ...

  • vertical angles are congruent
  • an exterior angle is equal to the sum of the opposite interior angles
  • the sum of angles forming a straight angle is 180°
  • the sum of angles in a triangle is 180°

__

Using these relations, we can find the unknown measures.

 a° = 60° . . . . . these are vertical angles

  51° +b° +110° = 180°   ⇒   b° = 180° -161° = 19° . . . . straight angle

  a° +b° +c° = 180°

  c° = 180° -60° -19° = 101° . . . . sum of angles in a triangle

  d° = 180° -101° = 79° . . . . . straight angle

 e° = c° -51° = 50° . . . . . c° is exterior to the triangle

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Answer:

DF = 38

GE = 40

Step-by-step explanation:

Given

DH = 2y + 6,

HF = 4x + 1,

HE = 3x + 2

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See attachment for parallelogram.

Required

Find GE and DF

From the attachment:

GH= HE

Substitute values for GH and HE

20 = 3x + 2

Subtract 2 from both sides

20-2 = 3x + 2-2

20-2 = 3x

18= 3x

3x = 18

Divide both sides by 3

x = \frac{18}{3}

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So:

GE = GH + GH

GE = 20 + 20

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To find DF, we find y first:

DH = HF

2y + 6 = 4x + 1

Subtract 6 from both sides

2y +6- 6 = 4x + 1-6

2y = 4x + 1-6

Substitute 6 for x

2y = 4*6 + 1-6

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y = \frac{19}{2}

y = 9.5

DF is then calculated as"

DF = DH + HF

DF = 2y+6 + 4x+1

Substitute values for x and y

DF = 2*9.5+6 + 4*3+1

DF = 38

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