Question

what is the value of x? write your answer as an integer or as a decimal rounded to the nearest tenth.

Explanation:

Step1: Apply exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $8x - 25=(3x + 23)+(3x - 12)$.

Step2: Simplify the right - hand side

Combine like terms on the right - hand side: $(3x + 23)+(3x - 12)=3x+3x + 23-12=6x + 11$. So the equation becomes $8x - 25=6x + 11$.

Step3: Isolate the variable x

Subtract $6x$ from both sides: $8x-6x - 25=6x-6x + 11$, which simplifies to $2x-25 = 11$. Then add 25 to both sides: $2x-25 + 25=11 + 25$, so $2x=36$.

Step4: Solve for x

Divide both sides by 2: $x=\frac{36}{2}=18$.

Answer:

18