Question

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

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(76+(4x - 11)+(4x + 3)=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \((4x+4x)+(76 - 11 + 3)=180\).
\(8x+(65 + 3)=180\), then \(8x+68 = 180\).

Step3: Solve for \(x\)

Subtract 68 from both sides: \(8x=180 - 68\), so \(8x=112\).
Divide both sides by 8: \(x=\frac{112}{8}\).

Answer:

\(x = 14\)