Question

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

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

Step2: Simplify the equation

First, calculate \(90 + 48 - 15\): \(90 + 48 = 138\), \(138 - 15 = 123\). So the equation becomes \(123 + 3x = 180\).

Step3: Solve for \(x\)

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

Answer:

\(x = 19\)