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 $(7x + 8)+102 + 28=180$.

Step2: Simplify the left - hand side of the equation

First, add the constant terms: $8+102 + 28=138$. The equation becomes $7x+138 = 180$.

Step3: Isolate the variable term

Subtract 138 from both sides of the equation: $7x=180 - 138$. So, $7x = 42$.

Step4: Solve for x

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

Answer:

$x = 6$