Question

find the value of x.

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $2x + 23=(3x - 57)+(x - 10)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(3x - 57)+(x - 10)=3x+x-57 - 10=4x-67$. So the equation becomes $2x + 23=4x-67$.

Step3: Isolate the variable terms

Subtract $2x$ from both sides: $2x+23-2x=4x - 67-2x$, which simplifies to $23 = 2x-67$.

Step4: Solve for $x$

Add 67 to both sides: $23 + 67=2x-67 + 67$, so $90 = 2x$. Then divide both sides by 2: $\frac{90}{2}=\frac{2x}{2}$, and $x = 45$.

Answer:

$x = 45$