Question

the measures of the angles of a triangle are shown in the figure below. solve for x.
answer attempt 1 out of 2
x =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we have the equation \((5x - 17)+56+(7x - 3)=180\).

Step2: Combine like - terms

First, combine the \(x\) terms and the constant terms: \((5x+7x)+(-17 + 56-3)=180\), which simplifies to \(12x+(36)=180\), or \(12x + 36=180\).

Step3: Isolate the variable term

Subtract 36 from both sides of the equation: \(12x+36 - 36=180 - 36\), resulting in \(12x=144\).

Step4: Solve for \(x\)

Divide both sides of the equation by 12: \(\frac{12x}{12}=\frac{144}{12}\), so \(x = 12\).

Answer:

\(x = 12\)