Question

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

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of a triangle is 180°. So, we have the equation \(61+(4x + 2)+45=180\).

Step2: Simplify the left - hand side

Combine like terms: \((61 + 2+45)+4x=180\), which gives \(108 + 4x=180\).

Step3: Isolate the variable term

Subtract 108 from both sides: \(4x=180 - 108\), so \(4x=72\).

Step4: Solve for x

Divide both sides by 4: \(x=\frac{72}{4}=18\).

Answer:

18