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 $(3x - 12)+60 + 90=180$.

Step2: Simplify the left - hand side

Combine like terms: $3x+( - 12 + 60+90)=3x + 138$. So the equation becomes $3x+138 = 180$.

Step3: Isolate the variable term

Subtract 138 from both sides: $3x=180 - 138$, which gives $3x = 42$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{42}{3}$.

Answer:

$x = 14$