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 triangle

The sum of the interior angles of a triangle is 180°. So, $(6x + 18)+30 + 90=180$.

Step2: Simplify the left - hand side

$6x+18 + 30+90=6x+(18 + 30+90)=6x + 138$. So, the equation becomes $6x+138 = 180$.

Step3: Isolate the term with x

Subtract 138 from both sides of the equation: $6x=180 - 138$.
$6x=42$.

Step4: Solve for x

Divide both sides by 6: $x=\frac{42}{6}$.
$x = 7$.

Answer:

$x = 7$