Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

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

Step2: Simplify the left - hand side of the equation

First, add the constant terms: \(74+62 - 1=135\). The equation becomes \(135 + 9x=180\).

Step3: Isolate the variable term

Subtract 135 from both sides of the equation: \(9x=180 - 135\), so \(9x = 45\).

Step4: Solve for x

Divide both sides of the equation by 9: \(x=\frac{45}{9}=5\).

Answer:

\(x = 5\)