Question

In AUVW, UW is extended through point W to point X, m VWX = (7x + 10)", mWUV = (2x + 20°, and mZUVW (2x + 17)". Find m VWX.

Answer 1

We have that the measure of an external angle in a triangle is the sum of the non-adjacent angles to this external angle. Then, we have that:

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

And now, we can solve this equation by summing like terms. Then, we have:

`2x+2x+17+20=7x+10\Rightarrow4x+37=7x+10`

We need to subtract 4x to both sides of the equation:

`4x-4x+37=7x-4x+10\Rightarrow0+37=3x+10`

Now, subtract 10 from both sides of the equation:

`37-10=3x+10-10\Rightarrow27=3x+0\Rightarrow3x=27`

Divide both sides of the equation by 3:

`(3x)/(3)=(27)/(3)\Rightarrow x=9`

And we have the value for x. However, we need to find the value for m< VWX = (7x+10). We need to plug the value of x in this equation. Then, we have:

`m\angle VWX=(7\cdot9+10)=63+10=73\Rightarrow m\angle VWX=73`

Hence, the value for m