Question

the measures of the angles of a triangle are shown in the figure below. solve for x. (3x - 15)° 48° (and a right angle symbol in the triangle)

Explanation:

Step1: Recall triangle angle sum

A triangle's angles sum to \(180^\circ\). This is a right triangle, so one angle is \(90^\circ\), another is \(48^\circ\), and the third is \((3x - 15)^\circ\). So, \((3x - 15)+90 + 48=180\).

Step2: Simplify the equation

Combine like terms: \(3x - 15+138 = 180\) → \(3x + 123 = 180\).

Step3: Solve for x

Subtract 123 from both sides: \(3x=180 - 123\) → \(3x = 57\). Divide by 3: \(x=\frac{57}{3}=19\).

Answer:

\(x = 19\)