Question

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

answer

x =

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(79^\circ + 45^\circ + (8x - 16)^\circ = 180^\circ\).

Step2: Simplify left side

Calculate \(79 + 45 - 16\): \(79 + 45 = 124\), \(124 - 16 = 108\). So, \(108 + 8x = 180\).

Step3: Solve for x

Subtract 108 from both sides: \(8x = 180 - 108 = 72\). Divide by 8: \(x = \frac{72}{8} = 9\).

Answer:

\(x = 9\)