Question

1. solve for x knowing that all three angles of the triangle should equal 180. (13x + 2)° (5x - 7)° (3x - 4)° o x = 12 o x = 4 o x = 9 o x = 16

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 \((13x + 2)+(5x - 7)+(3x - 4)=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((13x+5x + 3x)+(2-7 - 4)=180\), which simplifies to \(21x-9 = 180\).

Step3: Isolate the variable term

Add 9 to both sides of the equation: \(21x-9 + 9=180 + 9\), resulting in \(21x=189\).

Step4: Solve for \(x\)

Divide both sides by 21: \(x=\frac{189}{21}=9\).

Answer:

\(x = 9\)