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 $(4x + 3)+90 + 63=180$.

Step2: Simplify the left - hand side

Combine like terms: $4x+(3 + 90+63)=4x + 156$. So the equation becomes $4x+156 = 180$.

Step3: Isolate the variable term

Subtract 156 from both sides of the equation: $4x=180 - 156$. So, $4x = 24$.

Step4: Solve for x

Divide both sides by 4: $x=\frac{24}{4}$.

Answer:

$x = 6$