Question

solve for x knowing that the sum of the remote - interior angles should equal the exterior angle. (19x - 18)° (7x + 1)° (10x - 9)° o x = 5 o x = 4 o x = 9 o x = 16

Explanation:

Step1: Recall exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $(19x - 18)=(7x + 1)+(10x - 9)$.

Step2: Simplify the right - hand side

$(7x + 1)+(10x - 9)=7x+1 + 10x-9=17x - 8$.
So the equation becomes $19x-18 = 17x - 8$.

Step3: Isolate the variable terms

Subtract $17x$ from both sides: $19x-17x-18=17x-17x - 8$, which simplifies to $2x-18=-8$.

Step4: Isolate the variable

Add 18 to both sides: $2x-18 + 18=-8 + 18$, so $2x = 10$.

Step5: Solve for x

Divide both sides by 2: $\frac{2x}{2}=\frac{10}{2}$, so $x = 5$.

Answer:

$x = 5$