Question

find the measure of each acute angle. 3x° = □° and 2x° = □°

Explanation:

Step1: Use the triangle angle - sum property

In a right - triangle, the sum of the two acute angles is \(90^{\circ}\). So, \(2x + 3x=90\).

Step2: Solve the equation for \(x\)

Combine like terms: \(5x = 90\). Then, divide both sides by \(5\): \(x=\frac{90}{5}=18\).

Step3: Find the measure of \(2x\) and \(3x\)

For \(2x\): Substitute \(x = 18\) into \(2x\), we get \(2\times18 = 36\).
For \(3x\): Substitute \(x = 18\) into \(3x\), we get \(3\times18=54\).

Answer:

\(3x = 54\) and \(2x = 36\)