2 years ago

AB is parallel to CD, a) Find the value of angle x. b) work out the value of angle y.

Mathematics

1 answer:

anastassius [24]2 years ago

4 0

Answer:

x=69° y=69°

Step-by-step explanation:

Angle x is an alternate angle so it is equal to the angle above it (69)

Angle y is in a co-interior angle so you do the equation 180-111 which equals 69°

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If B is the midpoint of AC, solve for x, and find the lengths of AB, BC, and AC.

Whitepunk [10]

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x = 2

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Step-by-step explanation:

Given that B is the midpoint of AC, then AB = ½ of AC.

AB is given as 3(3x - 1),

AC = 5(2x + 2),

Therefore:

$3(3x - 1) = \frac{1}{2}*5(2x + 2)$

Solve for x

$9x - 3 = \frac{5}{2}(2x + 2)$

Multiply both sides by 2

$2(9x - 3) = \frac{5}{2}(2x + 2)*2$

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$18x - 6 = 10x + 10$

$18x - 10x = 6 + 10$

$8x = 16$

Divide both sides by 8

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$AB = BC = 3(3x - 1)$

Plug in the value of x

$AB = BC = 3(3(2) - 1)$

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$AC = 5(2(2) + 2)$

$AC = 5(4 + 2) = 5(6) = 30$

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