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 $(6x + 18)+30 + 90=180$.

Step2: Simplify the left - hand side

Combine like terms: $6x+18 + 30+90=6x+(18 + 30+90)=6x + 138$. So the equation becomes $6x+138 = 180$.

Step3: Isolate the variable term

Subtract 138 from both sides of the equation: $6x+138-138=180 - 138$, which simplifies to $6x=42$.

Step4: Solve for x

Divide both sides of the equation by 6: $\frac{6x}{6}=\frac{42}{6}$, so $x = 7$.

Answer:

$x = 7$