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3 years ago

PLEASE HELP ME WITH NUMBER 10

Mathematics

2 answers:

Maru [420]3 years ago

6 0

Answer:

Step-by-step explanation:

For those 2 lines to parallel to each other, then the 2 angles have to be alternate interior and have to be congruent. The value of x that makes them congruent is found by setting the 2 expressions equal to each other and solving for x:

$6x+42=18x-12$ and

$54=12x$ so

x = 4.5

Fittoniya [83]3 years ago

5 0

Answer:

4.5

Step-by-step explanation:

The two angles are equal

This means that: 6x + 42 = 18x - 12

Rearrange the equation to get x on one side and the integers on the other.

42 + 12 = 18x - 6x

54 = 12x

54/12 = x

x = 9/2 = 4.5

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FG ∥ CB, A ∈ FG, D ∈ AB, E ∈ AC

andrey2020 [161]

Answer:

The value of x is $31^{\circ}$ .

Step-by-step explanation:

Please look at the figure attached to get more clear solution.

We have given:

FG||CB

And the line that cut the parallel line is transversal so, here BA is transversal

And alternate interior angles on transverse line are equal

So, ∠1=∠4

And ∠4= $28^{\circ}$

Hence, ∠1=∠4= $28^{\circ}$

And On FG the sum of angles will be $180^{\circ}$

∠3+∠2+∠1= $180^{\circ}$

$90^{\circ}$ +∠2+ $28^{\circ}$ = $180^{\circ}$

Hence, ∠2= $62^{\circ}$

Now, we know that the sum of interior angles is equal to the exterior angle:

Therefore, ∠2+∠5=∠6+∠7

$62^{\circ}+3x=x+4x$

On simplification we get:

$2x=62^{\circ}$

$x=31^{\circ}$

Hence, the value of x is $31^{\circ}$ .

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