Question

the measures of the angles of a triangle are shown in the figure below. solve for x.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, we have the equation $(9x - 1)+62 + 74=180$.

Step2: Simplify the left - hand side

Combine like terms: $(9x-1)+62 + 74=9x+( - 1+62 + 74)=9x + 135$. So the equation becomes $9x+135 = 180$.

Step3: Isolate the variable term

Subtract 135 from both sides of the equation: $9x+135-135=180 - 135$, which simplifies to $9x=45$.

Step4: Solve for x

Divide both sides by 9: $\frac{9x}{9}=\frac{45}{9}$, so $x = 5$.

Answer:

$x = 5$