Question

find the measure of each acute angle.
(3x + 2)° = \square ° and x° = \square °

Explanation:

Step1: Recall triangle angle sum

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

Step2: Solve for \(x\)

Simplify the equation: \(4x + 2 = 90\). Subtract 2: \(4x = 88\). Divide by 4: \(x = 22\).

Step3: Find \(3x + 2\)

Substitute \(x = 22\) into \(3x + 2\): \(3(22)+2 = 66 + 2 = 68\).

Answer:

\((3x + 2)^\circ = \boldsymbol{68}^\circ\) and \(x^\circ = \boldsymbol{22}^\circ\)