Question

solve for x.

Explanation:

Step1: Apply exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle $ABC$, the exterior angle is $3x + 1$, and the two non - adjacent interior angles are $31^{\circ}$ and $118^{\circ}$. So, we can write the equation $3x+1=31 + 118$.

Step2: Simplify the right - hand side

Calculate the sum of the angles on the right - hand side: $31+118 = 149$. So the equation becomes $3x+1 = 149$.

Step3: Solve for $x$

Subtract 1 from both sides of the equation: $3x=149 - 1$, which gives $3x=148$. Then divide both sides by 3: $x=\frac{148}{3}$.

Answer:

$x=\frac{148}{3}$