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

1 Answer

3 votes

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,

In AUVW, UW is extended through point W to point X, mZUVW (3x + 16)", mWUV = (2x-example-1
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