Solved on Feb 24, 2024

Find the value of $x$ in an isosceles trapezoid $VWXY$ where $VX=3x+85$ and $WY=4x+68$ .

STEP 1

Assumptions
1. Quadrilateral $VWXY$ is an isosceles trapezoid.
2. The lengths of the non-parallel sides (legs) of an isosceles trapezoid are equal.
3. $VX = 3x + 85$ is the length of one leg.
4. $WY = 4x + 68$ is the length of the other leg.

STEP 2

Since $VWXY$ is an isosceles trapezoid, the lengths of its legs $VX$ and $WY$ are equal.
$VX = WY$

STEP 3

Substitute the given expressions for $VX$ and $WY$ into the equation from STEP_2.
$(3x + 85) = (4x + 68)$

STEP 4

To find the value of $x$ , we need to solve the equation for $x$ . Start by subtracting $3x$ from both sides of the equation to get the $x$ terms on one side.
$85 = x + 68$

STEP 5

Now subtract $68$ from both sides of the equation to isolate $x$ .
$85 - 68 = x$

STEP 6

Calculate the value of $x$ .
$x = 85 - 68 = 17$
The value of $x$ is 17.

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Find the value of $x$ in an isosceles trapezoid $VWXY$ where $VX=3x+85$ and $WY=4x+68$ .

STEP 1

Assumptions
1. Quadrilateral $VWXY$ is an isosceles trapezoid.
2. The lengths of the non-parallel sides (legs) of an isosceles trapezoid are equal.
3. $VX = 3x + 85$ is the length of one leg.
4. $WY = 4x + 68$ is the length of the other leg.

STEP 2

Since $VWXY$ is an isosceles trapezoid, the lengths of its legs $VX$ and $WY$ are equal.
$VX = WY$

STEP 3

Substitute the given expressions for $VX$ and $WY$ into the equation from STEP_2.
$(3x + 85) = (4x + 68)$

STEP 4

To find the value of $x$ , we need to solve the equation for $x$ . Start by subtracting $3x$ from both sides of the equation to get the $x$ terms on one side.
$85 = x + 68$

STEP 5

Now subtract $68$ from both sides of the equation to isolate $x$ .
$85 - 68 = x$

STEP 6

Calculate the value of $x$ .
$x = 85 - 68 = 17$
The value of $x$ is 17.

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Find the value of xxx in an isosceles trapezoid VWXYVWXYVWXY where VX=3x+85VX=3x+85VX=3x+85 and WY=4x+68WY=4x+68WY=4x+68.

STEP 1

Assumptions1. Quadrilateral VWXYVWXYVWXY is an isosceles trapezoid.2. The lengths of the non-parallel sides (legs) of an isosceles trapezoid are equal.3. VX=3x+85VX = 3x + 85VX=3x+85 is the length of one leg.4. WY=4x+68WY = 4x + 68WY=4x+68 is the length of the other leg.

STEP 2

Since VWXYVWXYVWXY is an isosceles trapezoid, the lengths of its legs VXVXVX and WYWYWY are equal.VX=WYVX = WYVX=WY

STEP 3

Substitute the given expressions for VXVXVX and WYWYWY into the equation from STEP_2.(3x+85)=(4x+68)(3x + 85) = (4x + 68)(3x+85)=(4x+68)

STEP 4

To find the value of xxx, we need to solve the equation for xxx. Start by subtracting 3x3x3x from both sides of the equation to get the xxx terms on one side.85=x+6885 = x + 6885=x+68

STEP 5

Now subtract 686868 from both sides of the equation to isolate xxx.85−68=x85 - 68 = x85−68=x

STEP 6

Calculate the value of xxx.x=85−68=17x = 85 - 68 = 17x=85−68=17The value of xxx is 17.

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Find the value of $x$ in an isosceles trapezoid $VWXY$ where $VX=3x+85$ and $WY=4x+68$ .

Assumptions
1. Quadrilateral $VWXY$ is an isosceles trapezoid.
2. The lengths of the non-parallel sides (legs) of an isosceles trapezoid are equal.
3. $VX = 3x + 85$ is the length of one leg.
4. $WY = 4x + 68$ is the length of the other leg.

Since $VWXY$ is an isosceles trapezoid, the lengths of its legs $VX$ and $WY$ are equal.
$VX = WY$

Substitute the given expressions for $VX$ and $WY$ into the equation from STEP_2.
$(3x + 85) = (4x + 68)$

To find the value of $x$ , we need to solve the equation for $x$ . Start by subtracting $3x$ from both sides of the equation to get the $x$ terms on one side.
$85 = x + 68$

Now subtract $68$ from both sides of the equation to isolate $x$ .
$85 - 68 = x$

Calculate the value of $x$ .
$x = 85 - 68 = 17$
The value of $x$ is 17.