Question

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 \(180^\circ\). So, \(83 + 61 + (4x + 16) = 180\).

Step2: Simplify the left side

Calculate \(83 + 61 + 16 = 160\), so the equation becomes \(160 + 4x = 180\).

Step3: Solve for x

Subtract 160 from both sides: \(4x = 180 - 160 = 20\). Then divide by 4: \(x = \frac{20}{4} = 5\).

Answer:

\(x = 5\)