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 $(8x + 3)+23 + 90=180$.

Step2: Simplify the left - hand side

Combine like terms: $8x+(3 + 23+90)=8x + 116$. So the equation becomes $8x+116 = 180$.

Step3: Isolate the variable term

Subtract 116 from both sides: $8x=180 - 116$. So, $8x=64$.

Step4: Solve for x

Divide both sides by 8: $x=\frac{64}{8}$.

Answer:

$x = 8$