Question

in δvwx, \\(\overline{vx}\\) is extended through point x to point y, \\(m\angle xvw = (x + 6)\degree\\), \\(m\angle wxy = (8x - 9)\degree\\), and \\(m\angle vwx = (2x + 10)\degree\\). what is the value of x?
answer attempt 1 out of 2
x =

Explanation:

Step1: Recall Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In $\triangle VWX$, $\angle WXY$ is an exterior angle, and $\angle XVW$ and $\angle VWX$ are the two non - adjacent interior angles. So, $m\angle WXY=m\angle XVW + m\angle VWX$.

Step2: Substitute the given angle measures

We know that $m\angle WXY=(8x - 9)^{\circ}$, $m\angle XVW=(x + 6)^{\circ}$, and $m\angle VWX=(2x+10)^{\circ}$. Substituting these into the equation from Step 1, we get:

$$8x-9=(x + 6)+(2x + 10)$$

Step3: Simplify the right - hand side

Simplify the right - hand side of the equation: $(x + 6)+(2x + 10)=x+2x+6 + 10=3x+16$. So the equation becomes $8x-9 = 3x+16$.

Step4: Solve for x

Subtract $3x$ from both sides: $8x-3x-9=3x - 3x+16$, which simplifies to $5x-9 = 16$. Then add 9 to both sides: $5x-9 + 9=16 + 9$, so $5x=25$. Divide both sides by 5: $\frac{5x}{5}=\frac{25}{5}$, which gives $x = 5$.

Answer:

\(x = 5\)