Question

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

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we have the equation $(4x + 2)+51 + 41=180$.

Step2: Simplify the left - hand side of the equation

First, combine like terms: $4x+(2 + 51+41)=4x + 94$. So the equation becomes $4x+94 = 180$.

Step3: Isolate the variable term

Subtract 94 from both sides of the equation: $4x+94−94=180 - 94$, which simplifies to $4x=86$.

Step4: Solve for x

Divide both sides of the equation by 4: $x=\frac{86}{4}=21.5$.

Answer:

$x = 21.5$