Question

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

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). This triangle is right - angled, so one angle is \(90^\circ\), another is \(67^\circ\), and the third is \((8x - 9)^\circ\). So we can set up the equation: \(90+67+(8x - 9)=180\).

Step2: Simplify the left - hand side

First, calculate \(90 + 67-9\): \(90+67 = 157\), then \(157-9 = 148\). So the equation becomes \(148 + 8x=180\).

Step3: Solve for x

Subtract 148 from both sides: \(8x=180 - 148\), \(180-148 = 32\), so \(8x = 32\). Then divide both sides by 8: \(x=\frac{32}{8}=4\).

Answer:

\(x = 4\)