Question

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

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(49+(6x + 6)+90=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(49+90+6x + 6=180\), which simplifies to \(145+6x=180\).

Step3: Isolate the variable term

Subtract \(145\) from both sides: \(6x=180 - 145\), so \(6x=35\).

Step4: Solve for \(x\)

Divide both sides by \(6\): \(x=\frac{35}{6}\approx5.83\).

Answer:

\(x = \frac{35}{6}\)