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 $(2x - 10)+109 + 43=180$.

Step2: Simplify the left - hand side

First, combine like terms: $(2x-10)+109 + 43=2x+( - 10+109 + 43)=2x + 142$. So the equation becomes $2x+142 = 180$.

Step3: Isolate the variable term

Subtract 142 from both sides of the equation: $2x+142-142=180 - 142$, which gives $2x=38$.

Step4: Solve for x

Divide both sides of the equation by 2: $\frac{2x}{2}=\frac{38}{2}$, so $x = 19$.

Answer:

$x = 19$