Question

determine the value of x.
figure is not drawn to scale
your answer
\\( x = 13 \\)
\\( x = 16 \\)
\\( x = 12 \\)
\\( x = 15 \\)

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((2x + 98)+(x + 19)+(3x-33)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((2x+x + 3x)+(98 + 19-33)=180\).
\(6x+(117 - 33)=180\).
\(6x + 84=180\).

Step3: Solve for \(x\)

Subtract 84 from both sides: \(6x=180 - 84\).
\(6x=96\).
Divide both sides by 6: \(x=\frac{96}{6}\).

Answer:

\(x = 16\)