Question

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

Explanation:

Step1: Use the property of right - angled triangle

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

Step2: Simplify the equation

Combine like terms: \(3x+x+2 = 90\), which gives \(4x+2=90\).

Step3: Solve for \(x\)

Subtract 2 from both sides: \(4x=90 - 2=88\). Then divide both sides by 4: \(x=\frac{88}{4}=22\).

Step4: Find the measure of \((3x + 2)\)

Substitute \(x = 22\) into \(3x+2\): \(3\times22+2=66 + 2=68\).

Answer:

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