Whats the value of x?

Mathematics

1 answer:

Nutka1998 [239]2 years ago

7 0

Answer:

x = 8 units, measure of angle AFE = 60 degrees, measure of angle CFD = 60 degrees

Step-by-step explanation:

Finding x:

You know all three of the given measures add up to 180 because they are on the same side of the line. Write an equation and solve for x.

6x + 2 + 8x + 6 + 7x + 4 = 180

21x = 168 --> x = 8

Angle AFE:

Substitute the value of x in the given measure.

7x + 4 = 7*8 + 4 = 56 + 4 = 60

Measure of angle CFD:

Angle AFE is it's vertical angle, so their measures (60 degrees) are equal.

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This pattern of question is always coming up. Since we can't easily guess, then let us set up simultaneous equation for the statements.

let the two numbers be x and y.

Multiply to 44.    x*y = 44 ..........(a)

Add up to 12. x + y = 12 .........(b)

From (b)

y = 12 - x .......(c)

Substitute (c) into (a)

x*y = 44

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-x² + 12x - 44 = 0.

Multiply both sides by -1

-1(-x² + 12x - 44) = -1*0

x² - 12x + 44 = 0.

This does not look factorizable, so let us just use quadratic formula

comparing to ax² + bx + c = 0, x² - 12x + 44 = 0, a = 1, b = -12, c = 44

x = (-b + √(b² - 4ac)) /2a   or (-b - √(b² - 4ac)) /2a

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x = (12 + √-32 )/ 2

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Where i is a complex number. Note the equation has two values. We shall include the second, that has negative sign before the square root.

x = (12 + √-32 )/ 2 or (12 - √-32 )/ 2

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When x = 6 - 2i√2, y = 12 - (6 - 2i√2) = 12 - 6 + 2i√2 = 6 + 2i√2

x = 6 + 2i√2, y = 6 - 2i√2

x = 6 - 2i√2, y = 6 + 2i√2

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