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DENIUS [597]
3 years ago
9

Findx. Assume the middle line is a midsegment in the problems below: HELPPPPPP

Mathematics
1 answer:
Andre45 [30]3 years ago
4 0

Answer:  x = 12

midsegment is 16 units long

bottom side is 32 units long

===============================================

Work Shown:

The midsegment 2x-8 is parallel to the bottom side 2x+8

The bottom side is twice as long compared to the midsegment (since the midsegment is half the length of the bottom side).

We can say

bottom side = 2*(midsegment)

2x+8 = 2*(2x-8)

2x+8 = 4x-16

2x-4x = -16-8

-2x = -24

x = -24/(-2)

x = 12

--------------------

Extra info:

Now that we know x, we can find the length of those segments

midsegment = 2x-8 = 2*12-8 = 24-8 = 16

bottom side = 2x+8 = 2*12+8 = 24+8 = 32

Note the bottom side (32) is exactly twice as long compared to the midsegment (16). This confirms we have the correct x value.

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m∠HKF = 87°

Solution:

Given data:

m(ar JF) = 135° and m(ar GH) = 42°

GJ is the diameter of the circle.

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⇒ m(ar JF) + m(ar FG) = 180°

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Subtract 135° from both sides of the equation.

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