Question

Find the value of x in each case. Give reasons to justify your solutions!

Answer 1

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Secondary School Math 35 points

Find the value of x in each case

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Answers

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tushar7863

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1.) x=60 because A is alternately equal to to E

2).=3x+40+11x-60+4x=180

=8x-4x+100=180

=4x=180-100

x=80/4

x=20

3).7x+3x+100=180

10x+100=180

10x=180-100

x=80/10

x=8

4).48+30+x=180

78+x=180

x=180-78

x=102

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Answer 2

the value of x is 31°

$\angle CDB = 4x = 4\times 31 = 128^{\circ}$

$\angle CDE= x =31^{\circ}$

$\angle AED = 3x = 3\times 31 = 93^{\circ}$

Step-by-step explanation:

here ,

$\angle 1 = \angle DAG = 28$° (alternate interior angles )

then,

$\angle 1 +\angle 2 + \angle CAF = 180$° (linear pair )

$28 + \angle 2 + 90 = 180$

$\angle 2 + 118 = 180\\\angle 2 = 190-118\\\angle 2 = 62$

therefore $\angle 2 = 62$°

$\angle BDC + \angle CDE +\angle EDA = 180$ (Linear pair)

$4x+x+\angle 3 = 180$

$5x+\angle 3 = 180\\\angle 3 = 180-5x$

now in triangle EDA

$3x+\angle 3 + \angle 2 = 180$ (angle sum property)

$3x+62+180-5x = 180\\62 - 2x = 0\\-2x= -62\\x = 31$

hence ,

the value of x is 31°

now, $\angle CDB = 4x = 4\times 31 = 128^{\circ}$

$\angle CDE= x =31^{\circ}$

$\angle AED = 3x = 3\times 31 = 93^{\circ}$

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