the diagram shows a triangle. what is the value of x? 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 $23x + 16x+63 = 180$.

Step2: Combine like - terms

Combining the $x$ terms, we get $(23 + 16)x+63=180$, which simplifies to $39x+63 = 180$.

Step3: Isolate the term with $x$

Subtract 63 from both sides of the equation: $39x=180 - 63$. So, $39x = 117$.

Step4: Solve for $x$

Divide both sides by 39: $x=\frac{117}{39}$. Thus, $x = 3$.

Answer:

$3$