Question

In AUVW, UW is extended through point W to point X, mZUVW (3x + 16)", mWUV = (2x + 8), and mZVWX = (8x – 18)". Find mZWUV.

Answer 1

Answer;

WUV = 36

Explanation:

Here is what we get when we draw the figures

Now we know that the sum of the interior angles of a triangle must equal 180 degrees; therefore,

`(2x+8)+(3x+16)+y=180^o\text{ }`

Also, angle y and VWX are supplementary; therefore,

`y+(8x-18)=180^o`

Now, solving for y in the above gives

`y=180+18-8x`
`y=198-8x`

Putting this value of y in the first equation gives

`(2x+8)+(3x+16)+(198-8x)=180^o\text{ }`

Expanding and simplifying the left-hand side gives

`-3x+222=180`

Subtracting 214 from both sides gives

`-3x=-42`

Finally, dividing both sides by -3 gives

`x=14.`

With the value of x in hand, we now find the measurement of WUV:

`\angle\text{WUV}=2x+8`
`\angle WUV=2(14)+8`
`\angle\text{WUV}=36^o`

Hence, WUV = 36,