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, $(3x - 15)+90 + 48=180$.

Step2: Simplify the left - hand side

Combine like terms: $3x-15 + 138=180$, which simplifies to $3x+123 = 180$.

Step3: Isolate the term with x

Subtract 123 from both sides: $3x=180 - 123$, so $3x = 57$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{57}{3}=19$.

Answer:

$x = 19$