Find m∠VWX. This is math homework

Question

In ΔUVW,  UW is extended through point W to point X,  m∠VWX=(7x+10)∘,  m∠WUV=(2x+20)∘,   and m∠UVW=(2x+17)∘.   Find m∠VWX.

Answer 1

Roman, Since the angles in a triangle have to add to 180°, there's something called the "Exterior Angle Theorem". An exterior angle is the angle created outside a triangle when you extend a side as is done here to side UW.

Because an exterior angle is supplementary to the interior angle it's next to, the two other interior angles added together equal the exterior angle measure. In your situation, after drawing the triangle, you can write

(2x+17)+(2x+20) = 7x+10.

4x+37 = 7x+10

Subtract 4x then 10 from both sides to get 27=3x, then divide to get 9=x.

Plug this into the equation for ∠VWX: 7(9)+10=73°.

I hope this helps! Geometry rocks!

Liz Z.

Answer 2

Draw a diagram.

angle UWV = 180 - (7x+10)

Since the degree measures of the interior angles of a triangle add up to 180, we have:

(180 - (7x + 10)) + (2x+20) + (2x+17) = 180

So, -3x + 27 = 0.

x = 9

angle VWX = 7x + 10 = 73 degrees